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mw-ui-icon-wikimedia-expand"></span> <span>开关历史子章节</span> </button> <ul id="toc-历史-sublist" class="vector-toc-list"> <li id="toc-古代" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#古代"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>古代</span> </div> </a> <ul id="toc-古代-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-中世纪" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#中世纪"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>中世纪</span> </div> </a> <ul id="toc-中世纪-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-近代" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#近代"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>近代</span> </div> </a> <ul id="toc-近代-sublist" class="vector-toc-list"> <li id="toc-費馬" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#費馬"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.1</span> <span>費馬</span> </div> </a> <ul id="toc-費馬-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-歐拉" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#歐拉"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3.2</span> <span>歐拉</span> </div> </a> <ul id="toc-歐拉-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> </ul> </li> <li id="toc-分支" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#分支"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>分支</span> </div> </a> <ul id="toc-分支-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-應用" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#應用"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>應用</span> </div> </a> <ul id="toc-應用-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-注释" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#注释"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>注释</span> </div> </a> <ul id="toc-注释-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考資料" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考資料"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>參考資料</span> </div> </a> <ul id="toc-參考資料-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-參考書目" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#參考書目"> <div class="vector-toc-text"> <span class="vector-toc-numb">7</span> <span>參考書目</span> </div> </a> <ul id="toc-參考書目-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-外部連結" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#外部連結"> <div class="vector-toc-text"> <span class="vector-toc-numb">8</span> <span>外部連結</span> </div> </a> <ul id="toc-外部連結-sublist" class="vector-toc-list"> </ul> </li> </ul> </div> </div> </nav> </div> </div> <div class="mw-content-container"> <main id="content" class="mw-body"> <header class="mw-body-header vector-page-titlebar"> <nav aria-label="目录" class="vector-toc-landmark"> <div id="vector-page-titlebar-toc" class="vector-dropdown vector-page-titlebar-toc vector-button-flush-left" > <input type="checkbox" id="vector-page-titlebar-toc-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="开关目录" > <label id="vector-page-titlebar-toc-label" for="vector-page-titlebar-toc-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only " aria-hidden="true" ><span class="vector-icon mw-ui-icon-listBullet mw-ui-icon-wikimedia-listBullet"></span> <span class="vector-dropdown-label-text">开关目录</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-titlebar-toc-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <h1 id="firstHeading" class="firstHeading mw-first-heading"><span class="mw-page-title-main">数论</span></h1> <div id="p-lang-btn" class="vector-dropdown mw-portlet mw-portlet-lang" > <input type="checkbox" id="p-lang-btn-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-p-lang-btn" class="vector-dropdown-checkbox mw-interlanguage-selector" aria-label="前往另一种语言写成的文章。114种语言可用" > <label id="p-lang-btn-label" for="p-lang-btn-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--action-progressive mw-portlet-lang-heading-114" aria-hidden="true" ><span class="vector-icon mw-ui-icon-language-progressive mw-ui-icon-wikimedia-language-progressive"></span> <span class="vector-dropdown-label-text">114种语言</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-af mw-list-item"><a href="https://af.wikipedia.org/wiki/Getalteorie" title="Getalteorie – 南非荷兰语" lang="af" hreflang="af" data-title="Getalteorie" data-language-autonym="Afrikaans" data-language-local-name="南非荷兰语" class="interlanguage-link-target"><span>Afrikaans</span></a></li><li class="interlanguage-link interwiki-als mw-list-item"><a href="https://als.wikipedia.org/wiki/Zahlentheorie" title="Zahlentheorie – 瑞士德语" lang="gsw" hreflang="gsw" data-title="Zahlentheorie" data-language-autonym="Alemannisch" data-language-local-name="瑞士德语" class="interlanguage-link-target"><span>Alemannisch</span></a></li><li class="interlanguage-link interwiki-an mw-list-item"><a href="https://an.wikipedia.org/wiki/Teor%C3%ADa_de_numeros" title="Teoría de numeros – 阿拉贡语" lang="an" hreflang="an" data-title="Teoría de numeros" data-language-autonym="Aragonés" data-language-local-name="阿拉贡语" class="interlanguage-link-target"><span>Aragonés</span></a></li><li class="interlanguage-link interwiki-ar mw-list-item"><a href="https://ar.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%D9%8A%D8%A9_%D8%A7%D9%84%D8%A3%D8%B9%D8%AF%D8%A7%D8%AF" title="نظرية الأعداد – 阿拉伯语" lang="ar" hreflang="ar" data-title="نظرية الأعداد" data-language-autonym="العربية" data-language-local-name="阿拉伯语" class="interlanguage-link-target"><span>العربية</span></a></li><li class="interlanguage-link interwiki-ary mw-list-item"><a href="https://ary.wikipedia.org/wiki/%D9%86%D8%B6%D8%B1%D9%8A%D8%A9_%D8%AF_%D9%84%D8%A3%D8%B9%D8%AF%D8%A7%D8%AF" title="نضرية د لأعداد – 摩洛哥阿拉伯文" lang="ary" hreflang="ary" data-title="نضرية د لأعداد" data-language-autonym="الدارجة" data-language-local-name="摩洛哥阿拉伯文" class="interlanguage-link-target"><span>الدارجة</span></a></li><li class="interlanguage-link interwiki-arz mw-list-item"><a href="https://arz.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%D9%8A%D9%87_%D8%A7%D9%84%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF" title="نظريه الاعداد – 埃及阿拉伯文" lang="arz" hreflang="arz" data-title="نظريه الاعداد" data-language-autonym="مصرى" data-language-local-name="埃及阿拉伯文" class="interlanguage-link-target"><span>مصرى</span></a></li><li class="interlanguage-link interwiki-as mw-list-item"><a href="https://as.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="সংখ্যাতত্ত্ব – 阿萨姆语" lang="as" hreflang="as" data-title="সংখ্যাতত্ত্ব" data-language-autonym="অসমীয়া" data-language-local-name="阿萨姆语" class="interlanguage-link-target"><span>অসমীয়া</span></a></li><li class="interlanguage-link interwiki-ast mw-list-item"><a href="https://ast.wikipedia.org/wiki/Teor%C3%ADa_de_n%C3%BAmberos" title="Teoría de númberos – 阿斯图里亚斯语" lang="ast" hreflang="ast" data-title="Teoría de númberos" data-language-autonym="Asturianu" data-language-local-name="阿斯图里亚斯语" class="interlanguage-link-target"><span>Asturianu</span></a></li><li class="interlanguage-link interwiki-az mw-list-item"><a href="https://az.wikipedia.org/wiki/%C6%8Fd%C9%99dl%C9%99r_n%C9%99z%C9%99riyy%C9%99si" title="Ədədlər nəzəriyyəsi – 阿塞拜疆语" lang="az" hreflang="az" data-title="Ədədlər nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="阿塞拜疆语" class="interlanguage-link-target"><span>Azərbaycanca</span></a></li><li class="interlanguage-link interwiki-ba mw-list-item"><a href="https://ba.wikipedia.org/wiki/%D2%BA%D0%B0%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D2%BB%D1%8B" title="Һандар теорияһы – 巴什基尔语" lang="ba" hreflang="ba" data-title="Һандар теорияһы" data-language-autonym="Башҡортса" data-language-local-name="巴什基尔语" class="interlanguage-link-target"><span>Башҡортса</span></a></li><li class="interlanguage-link interwiki-bat-smg mw-list-item"><a href="https://bat-smg.wikipedia.org/wiki/Skaitliu_teuor%C4%97j%C4%97" title="Skaitliu teuorėjė – 薩莫吉希亞文" lang="sgs" hreflang="sgs" data-title="Skaitliu teuorėjė" data-language-autonym="Žemaitėška" data-language-local-name="薩莫吉希亞文" class="interlanguage-link-target"><span>Žemaitėška</span></a></li><li class="interlanguage-link interwiki-bcl mw-list-item"><a href="https://bcl.wikipedia.org/wiki/Teorya_nin_bilang" title="Teorya nin bilang – Central Bikol" lang="bcl" hreflang="bcl" data-title="Teorya nin bilang" data-language-autonym="Bikol Central" data-language-local-name="Central Bikol" class="interlanguage-link-target"><span>Bikol Central</span></a></li><li class="interlanguage-link interwiki-be mw-list-item"><a href="https://be.wikipedia.org/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D0%B0%D1%9E" title="Тэорыя лікаў – 白俄罗斯语" lang="be" hreflang="be" data-title="Тэорыя лікаў" data-language-autonym="Беларуская" data-language-local-name="白俄罗斯语" class="interlanguage-link-target"><span>Беларуская</span></a></li><li class="interlanguage-link interwiki-be-x-old mw-list-item"><a href="https://be-tarask.wikipedia.org/wiki/%D0%A2%D1%8D%D0%BE%D1%80%D1%8B%D1%8F_%D0%BB%D1%96%D0%BA%D0%B0%D1%9E" title="Тэорыя лікаў – Belarusian (Taraškievica orthography)" lang="be-tarask" hreflang="be-tarask" data-title="Тэорыя лікаў" data-language-autonym="Беларуская (тарашкевіца)" data-language-local-name="Belarusian (Taraškievica orthography)" class="interlanguage-link-target"><span>Беларуская (тарашкевіца)</span></a></li><li class="interlanguage-link interwiki-bg mw-list-item"><a href="https://bg.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D0%BD%D0%B0_%D1%87%D0%B8%D1%81%D0%BB%D0%B0%D1%82%D0%B0" title="Теория на числата – 保加利亚语" lang="bg" hreflang="bg" data-title="Теория на числата" data-language-autonym="Български" data-language-local-name="保加利亚语" class="interlanguage-link-target"><span>Български</span></a></li><li class="interlanguage-link interwiki-bn mw-list-item"><a href="https://bn.wikipedia.org/wiki/%E0%A6%B8%E0%A6%82%E0%A6%96%E0%A7%8D%E0%A6%AF%E0%A6%BE%E0%A6%A4%E0%A6%A4%E0%A7%8D%E0%A6%A4%E0%A7%8D%E0%A6%AC" title="সংখ্যাতত্ত্ব – 孟加拉语" lang="bn" hreflang="bn" data-title="সংখ্যাতত্ত্ব" data-language-autonym="বাংলা" data-language-local-name="孟加拉语" class="interlanguage-link-target"><span>বাংলা</span></a></li><li class="interlanguage-link interwiki-br mw-list-item"><a href="https://br.wikipedia.org/wiki/Damkaniezh_an_nivero%C3%B9" title="Damkaniezh an niveroù – 布列塔尼语" lang="br" hreflang="br" data-title="Damkaniezh an niveroù" data-language-autonym="Brezhoneg" data-language-local-name="布列塔尼语" class="interlanguage-link-target"><span>Brezhoneg</span></a></li><li class="interlanguage-link interwiki-bs mw-list-item"><a href="https://bs.wikipedia.org/wiki/Teorija_brojeva" title="Teorija brojeva – 波斯尼亚语" lang="bs" hreflang="bs" data-title="Teorija brojeva" data-language-autonym="Bosanski" data-language-local-name="波斯尼亚语" class="interlanguage-link-target"><span>Bosanski</span></a></li><li class="interlanguage-link interwiki-ca mw-list-item"><a href="https://ca.wikipedia.org/wiki/Teoria_de_nombres" title="Teoria de nombres – 加泰罗尼亚语" lang="ca" hreflang="ca" data-title="Teoria de nombres" data-language-autonym="Català" data-language-local-name="加泰罗尼亚语" class="interlanguage-link-target"><span>Català</span></a></li><li class="interlanguage-link interwiki-ckb mw-list-item"><a href="https://ckb.wikipedia.org/wiki/%D8%AA%DB%8C%DB%86%D8%B1%DB%8C%DB%8C_%DA%98%D9%85%D8%A7%D8%B1%DB%95" title="تیۆریی ژمارە – 中库尔德语" lang="ckb" hreflang="ckb" data-title="تیۆریی ژمارە" data-language-autonym="کوردی" data-language-local-name="中库尔德语" class="interlanguage-link-target"><span>کوردی</span></a></li><li class="interlanguage-link interwiki-cs mw-list-item"><a href="https://cs.wikipedia.org/wiki/Teorie_%C4%8D%C3%ADsel" title="Teorie čísel – 捷克语" lang="cs" hreflang="cs" data-title="Teorie čísel" data-language-autonym="Čeština" data-language-local-name="捷克语" class="interlanguage-link-target"><span>Čeština</span></a></li><li class="interlanguage-link interwiki-cv mw-list-item"><a href="https://cv.wikipedia.org/wiki/%D0%A5%D0%B8%D1%81%D0%B5%D0%BF%D1%81%D0%B5%D0%BD_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D0%B9%C4%95" title="Хисепсен теорийĕ – 楚瓦什语" lang="cv" hreflang="cv" data-title="Хисепсен теорийĕ" data-language-autonym="Чӑвашла" data-language-local-name="楚瓦什语" class="interlanguage-link-target"><span>Чӑвашла</span></a></li><li class="interlanguage-link interwiki-cy mw-list-item"><a href="https://cy.wikipedia.org/wiki/Damcaniaeth_rhifau" title="Damcaniaeth rhifau – 威尔士语" lang="cy" hreflang="cy" data-title="Damcaniaeth rhifau" data-language-autonym="Cymraeg" data-language-local-name="威尔士语" class="interlanguage-link-target"><span>Cymraeg</span></a></li><li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/Talteori" title="Talteori – 丹麦语" lang="da" hreflang="da" data-title="Talteori" data-language-autonym="Dansk" data-language-local-name="丹麦语" class="interlanguage-link-target"><span>Dansk</span></a></li><li class="interlanguage-link interwiki-de mw-list-item"><a href="https://de.wikipedia.org/wiki/Zahlentheorie" title="Zahlentheorie – 德语" lang="de" hreflang="de" data-title="Zahlentheorie" data-language-autonym="Deutsch" data-language-local-name="德语" class="interlanguage-link-target"><span>Deutsch</span></a></li><li class="interlanguage-link interwiki-el mw-list-item"><a href="https://el.wikipedia.org/wiki/%CE%98%CE%B5%CF%89%CF%81%CE%AF%CE%B1_%CE%B1%CF%81%CE%B9%CE%B8%CE%BC%CF%8E%CE%BD" title="Θεωρία αριθμών – 希腊语" lang="el" hreflang="el" data-title="Θεωρία αριθμών" data-language-autonym="Ελληνικά" data-language-local-name="希腊语" class="interlanguage-link-target"><span>Ελληνικά</span></a></li><li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Number_theory" title="Number theory – 英语" lang="en" hreflang="en" data-title="Number theory" data-language-autonym="English" data-language-local-name="英语" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-eo mw-list-item"><a href="https://eo.wikipedia.org/wiki/Nombroteorio" title="Nombroteorio – 世界语" lang="eo" hreflang="eo" data-title="Nombroteorio" data-language-autonym="Esperanto" data-language-local-name="世界语" class="interlanguage-link-target"><span>Esperanto</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/Teor%C3%ADa_de_n%C3%BAmeros" title="Teoría de números – 西班牙语" lang="es" hreflang="es" data-title="Teoría de números" data-language-autonym="Español" data-language-local-name="西班牙语" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-et mw-list-item"><a href="https://et.wikipedia.org/wiki/Arvuteooria" title="Arvuteooria – 爱沙尼亚语" lang="et" hreflang="et" data-title="Arvuteooria" data-language-autonym="Eesti" data-language-local-name="爱沙尼亚语" class="interlanguage-link-target"><span>Eesti</span></a></li><li class="interlanguage-link interwiki-eu mw-list-item"><a href="https://eu.wikipedia.org/wiki/Zenbakien_teoria" title="Zenbakien teoria – 巴斯克语" lang="eu" hreflang="eu" data-title="Zenbakien teoria" data-language-autonym="Euskara" data-language-local-name="巴斯克语" class="interlanguage-link-target"><span>Euskara</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%DB%8C%D9%87_%D8%A7%D8%B9%D8%AF%D8%A7%D8%AF" title="نظریه اعداد – 波斯语" lang="fa" hreflang="fa" data-title="نظریه اعداد" data-language-autonym="فارسی" data-language-local-name="波斯语" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Lukuteoria" title="Lukuteoria – 芬兰语" lang="fi" hreflang="fi" data-title="Lukuteoria" data-language-autonym="Suomi" data-language-local-name="芬兰语" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fiu-vro mw-list-item"><a href="https://fiu-vro.wikipedia.org/wiki/Arvoteooria" title="Arvoteooria – 佛羅文" lang="vro" hreflang="vro" data-title="Arvoteooria" data-language-autonym="Võro" data-language-local-name="佛羅文" class="interlanguage-link-target"><span>Võro</span></a></li><li class="interlanguage-link interwiki-fj mw-list-item"><a href="https://fj.wikipedia.org/wiki/Naba_icavacava" title="Naba icavacava – 斐济语" lang="fj" hreflang="fj" data-title="Naba icavacava" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="斐济语" class="interlanguage-link-target"><span>Na Vosa Vakaviti</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Th%C3%A9orie_des_nombres" title="Théorie des nombres – 法语" lang="fr" hreflang="fr" data-title="Théorie des nombres" data-language-autonym="Français" data-language-local-name="法语" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-frr mw-list-item"><a href="https://frr.wikipedia.org/wiki/Taalenteorii" title="Taalenteorii – 北弗里西亚语" lang="frr" hreflang="frr" data-title="Taalenteorii" data-language-autonym="Nordfriisk" data-language-local-name="北弗里西亚语" class="interlanguage-link-target"><span>Nordfriisk</span></a></li><li class="interlanguage-link interwiki-ga mw-list-item"><a href="https://ga.wikipedia.org/wiki/Uimhirtheoiric" title="Uimhirtheoiric – 爱尔兰语" lang="ga" hreflang="ga" data-title="Uimhirtheoiric" data-language-autonym="Gaeilge" data-language-local-name="爱尔兰语" class="interlanguage-link-target"><span>Gaeilge</span></a></li><li class="interlanguage-link interwiki-gan mw-list-item"><a href="https://gan.wikipedia.org/wiki/%E6%95%B8%E8%AB%96" title="數論 – 赣语" lang="gan" hreflang="gan" data-title="數論" data-language-autonym="贛語" data-language-local-name="赣语" class="interlanguage-link-target"><span>贛語</span></a></li><li class="interlanguage-link interwiki-gcr mw-list-item"><a href="https://gcr.wikipedia.org/wiki/T%C3%A9ori_di_s%C3%A9_nonm" title="Téori di sé nonm – Guianan Creole" lang="gcr" hreflang="gcr" data-title="Téori di sé nonm" data-language-autonym="Kriyòl gwiyannen" data-language-local-name="Guianan Creole" class="interlanguage-link-target"><span>Kriyòl gwiyannen</span></a></li><li class="interlanguage-link interwiki-gl mw-list-item"><a href="https://gl.wikipedia.org/wiki/Teor%C3%ADa_de_n%C3%BAmeros" title="Teoría de números – 加利西亚语" lang="gl" hreflang="gl" data-title="Teoría de números" data-language-autonym="Galego" data-language-local-name="加利西亚语" class="interlanguage-link-target"><span>Galego</span></a></li><li class="interlanguage-link interwiki-gu mw-list-item"><a href="https://gu.wikipedia.org/wiki/%E0%AA%B8%E0%AA%82%E0%AA%96%E0%AB%8D%E0%AA%AF%E0%AA%BE_%E0%AA%B8%E0%AA%BF%E0%AA%A6%E0%AB%8D%E0%AA%A7%E0%AA%BE%E0%AA%82%E0%AA%A4" title="સંખ્યા સિદ્ધાંત – 古吉拉特语" lang="gu" hreflang="gu" data-title="સંખ્યા સિદ્ધાંત" data-language-autonym="ગુજરાતી" data-language-local-name="古吉拉特语" class="interlanguage-link-target"><span>ગુજરાતી</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%AA%D7%95%D7%A8%D7%AA_%D7%94%D7%9E%D7%A1%D7%A4%D7%A8%D7%99%D7%9D" title="תורת המספרים – 希伯来语" lang="he" hreflang="he" data-title="תורת המספרים" data-language-autonym="עברית" data-language-local-name="希伯来语" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE_%E0%A4%B8%E0%A4%BF%E0%A4%A6%E0%A5%8D%E0%A4%A7%E0%A4%BE%E0%A4%A8%E0%A5%8D%E0%A4%A4" title="संख्या सिद्धान्त – 印地语" lang="hi" hreflang="hi" data-title="संख्या सिद्धान्त" data-language-autonym="हिन्दी" data-language-local-name="印地语" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hif mw-list-item"><a href="https://hif.wikipedia.org/wiki/Number_theory" title="Number theory – 斐濟印地文" lang="hif" hreflang="hif" data-title="Number theory" data-language-autonym="Fiji Hindi" data-language-local-name="斐濟印地文" class="interlanguage-link-target"><span>Fiji Hindi</span></a></li><li class="interlanguage-link interwiki-hr mw-list-item"><a href="https://hr.wikipedia.org/wiki/Teorija_brojeva" title="Teorija brojeva – 克罗地亚语" lang="hr" hreflang="hr" data-title="Teorija brojeva" data-language-autonym="Hrvatski" data-language-local-name="克罗地亚语" class="interlanguage-link-target"><span>Hrvatski</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Sz%C3%A1melm%C3%A9let" title="Számelmélet – 匈牙利语" lang="hu" hreflang="hu" data-title="Számelmélet" data-language-autonym="Magyar" data-language-local-name="匈牙利语" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-hy mw-list-item"><a href="https://hy.wikipedia.org/wiki/%D4%B9%D5%BE%D5%A5%D6%80%D5%AB_%D5%BF%D5%A5%D5%BD%D5%B8%D6%82%D5%A9%D5%B5%D5%B8%D6%82%D5%B6" title="Թվերի տեսություն – 亚美尼亚语" lang="hy" hreflang="hy" data-title="Թվերի տեսություն" data-language-autonym="Հայերեն" data-language-local-name="亚美尼亚语" class="interlanguage-link-target"><span>Հայերեն</span></a></li><li class="interlanguage-link interwiki-ia mw-list-item"><a href="https://ia.wikipedia.org/wiki/Theoria_de_numeros" title="Theoria de numeros – 国际语" lang="ia" hreflang="ia" data-title="Theoria de numeros" data-language-autonym="Interlingua" data-language-local-name="国际语" class="interlanguage-link-target"><span>Interlingua</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/Teori_bilangan" title="Teori bilangan – 印度尼西亚语" lang="id" hreflang="id" data-title="Teori bilangan" data-language-autonym="Bahasa Indonesia" data-language-local-name="印度尼西亚语" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-io mw-list-item"><a href="https://io.wikipedia.org/wiki/Teorio_di_nombri" title="Teorio di nombri – 伊多语" lang="io" hreflang="io" data-title="Teorio di nombri" data-language-autonym="Ido" data-language-local-name="伊多语" class="interlanguage-link-target"><span>Ido</span></a></li><li class="interlanguage-link interwiki-is mw-list-item"><a href="https://is.wikipedia.org/wiki/Talnafr%C3%A6%C3%B0i" title="Talnafræði – 冰岛语" lang="is" hreflang="is" data-title="Talnafræði" data-language-autonym="Íslenska" data-language-local-name="冰岛语" class="interlanguage-link-target"><span>Íslenska</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Teoria_dei_numeri" title="Teoria dei numeri – 意大利语" lang="it" hreflang="it" data-title="Teoria dei numeri" data-language-autonym="Italiano" data-language-local-name="意大利语" class="interlanguage-link-target"><span>Italiano</span></a></li><li class="interlanguage-link interwiki-ja mw-list-item"><a href="https://ja.wikipedia.org/wiki/%E6%95%B0%E8%AB%96" title="数論 – 日语" lang="ja" hreflang="ja" data-title="数論" data-language-autonym="日本語" data-language-local-name="日语" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-jam mw-list-item"><a href="https://jam.wikipedia.org/wiki/Nomba_tiori" title="Nomba tiori – 牙買加克里奧爾英文" lang="jam" hreflang="jam" data-title="Nomba tiori" data-language-autonym="Patois" data-language-local-name="牙買加克里奧爾英文" class="interlanguage-link-target"><span>Patois</span></a></li><li class="interlanguage-link interwiki-jbo mw-list-item"><a href="https://jbo.wikipedia.org/wiki/nacycmaci" title="nacycmaci – 逻辑语" lang="jbo" hreflang="jbo" data-title="nacycmaci" data-language-autonym="La .lojban." data-language-local-name="逻辑语" class="interlanguage-link-target"><span>La .lojban.</span></a></li><li class="interlanguage-link interwiki-jv mw-list-item"><a href="https://jv.wikipedia.org/wiki/T%C3%A9ori_wilangan" title="Téori wilangan – 爪哇语" lang="jv" hreflang="jv" data-title="Téori wilangan" data-language-autonym="Jawa" data-language-local-name="爪哇语" class="interlanguage-link-target"><span>Jawa</span></a></li><li class="interlanguage-link interwiki-ka mw-list-item"><a href="https://ka.wikipedia.org/wiki/%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%95%E1%83%97%E1%83%90_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90" title="რიცხვთა თეორია – 格鲁吉亚语" lang="ka" hreflang="ka" data-title="რიცხვთა თეორია" data-language-autonym="ქართული" data-language-local-name="格鲁吉亚语" class="interlanguage-link-target"><span>ქართული</span></a></li><li class="interlanguage-link interwiki-kk mw-list-item"><a href="https://kk.wikipedia.org/wiki/%D0%A1%D0%B0%D0%BD%D0%B4%D0%B0%D1%80_%D1%82%D0%B5%D0%BE%D1%80%D0%B8%D1%8F%D1%81%D1%8B" title="Сандар теориясы – 哈萨克语" lang="kk" hreflang="kk" data-title="Сандар теориясы" data-language-autonym="Қазақша" data-language-local-name="哈萨克语" class="interlanguage-link-target"><span>Қазақша</span></a></li><li class="interlanguage-link interwiki-kn mw-list-item"><a href="https://kn.wikipedia.org/wiki/%E0%B2%B8%E0%B2%82%E0%B2%96%E0%B3%8D%E0%B2%AF%E0%B2%BE%E0%B2%B8%E0%B2%BF%E0%B2%A6%E0%B3%8D%E0%B2%A7%E0%B2%BE%E0%B2%82%E0%B2%A4" title="ಸಂಖ್ಯಾಸಿದ್ಧಾಂತ – 卡纳达语" lang="kn" hreflang="kn" data-title="ಸಂಖ್ಯಾಸಿದ್ಧಾಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="卡纳达语" class="interlanguage-link-target"><span>ಕನ್ನಡ</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/%EC%88%98%EB%A1%A0" title="수론 – 韩语" lang="ko" hreflang="ko" data-title="수론" data-language-autonym="한국어" data-language-local-name="韩语" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-ku mw-list-item"><a href="https://ku.wikipedia.org/wiki/B%C3%AErdoza_jimare" title="Bîrdoza jimare – 库尔德语" lang="ku" hreflang="ku" data-title="Bîrdoza jimare" data-language-autonym="Kurdî" data-language-local-name="库尔德语" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="典范条目"><a href="https://la.wikipedia.org/wiki/Theoria_numerorum" title="Theoria numerorum – 拉丁语" lang="la" hreflang="la" data-title="Theoria numerorum" data-language-autonym="Latina" data-language-local-name="拉丁语" class="interlanguage-link-target"><span>Latina</span></a></li><li class="interlanguage-link interwiki-lb mw-list-item"><a href="https://lb.wikipedia.org/wiki/Zuelentheorie" title="Zuelentheorie – 卢森堡语" lang="lb" hreflang="lb" data-title="Zuelentheorie" data-language-autonym="Lëtzebuergesch" data-language-local-name="卢森堡语" class="interlanguage-link-target"><span>Lëtzebuergesch</span></a></li><li class="interlanguage-link interwiki-lmo mw-list-item"><a href="https://lmo.wikipedia.org/wiki/Teoria_di_numer" title="Teoria di numer – 倫巴底文" lang="lmo" hreflang="lmo" data-title="Teoria di numer" data-language-autonym="Lombard" data-language-local-name="倫巴底文" class="interlanguage-link-target"><span>Lombard</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Skai%C4%8Di%C5%B3_teorija" title="Skaičių teorija – 立陶宛语" lang="lt" hreflang="lt" data-title="Skaičių teorija" data-language-autonym="Lietuvių" data-language-local-name="立陶宛语" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/Skait%C4%BCu_teorija" title="Skaitļu teorija – 拉脱维亚语" lang="lv" hreflang="lv" data-title="Skaitļu teorija" data-language-autonym="Latviešu" data-language-local-name="拉脱维亚语" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-mk mw-list-item"><a href="https://mk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%BD%D0%B0_%D0%B1%D1%80%D0%BE%D0%B5%D0%B2%D0%B8%D1%82%D0%B5" title="Теорија на броевите – 马其顿语" lang="mk" hreflang="mk" data-title="Теорија на броевите" data-language-autonym="Македонски" data-language-local-name="马其顿语" class="interlanguage-link-target"><span>Македонски</span></a></li><li class="interlanguage-link interwiki-ml mw-list-item"><a href="https://ml.wikipedia.org/wiki/%E0%B4%B8%E0%B4%82%E0%B4%96%E0%B5%8D%E0%B4%AF%E0%B4%BE%E0%B4%B8%E0%B4%BF%E0%B4%A6%E0%B5%8D%E0%B4%A7%E0%B4%BE%E0%B4%A8%E0%B5%8D%E0%B4%A4%E0%B4%82" title="സംഖ്യാസിദ്ധാന്തം – 马拉雅拉姆语" lang="ml" hreflang="ml" data-title="സംഖ്യാസിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="马拉雅拉姆语" class="interlanguage-link-target"><span>മലയാളം</span></a></li><li class="interlanguage-link interwiki-mn mw-list-item"><a href="https://mn.wikipedia.org/wiki/%D0%A2%D0%BE%D0%BE%D0%BD%D1%8B_%D0%BE%D0%BD%D0%BE%D0%BB" title="Тооны онол – 蒙古语" lang="mn" hreflang="mn" data-title="Тооны онол" data-language-autonym="Монгол" data-language-local-name="蒙古语" class="interlanguage-link-target"><span>Монгол</span></a></li><li class="interlanguage-link interwiki-mr mw-list-item"><a href="https://mr.wikipedia.org/wiki/%E0%A4%85%E0%A4%82%E0%A4%95%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0" title="अंकशास्त्र – 马拉地语" lang="mr" hreflang="mr" data-title="अंकशास्त्र" data-language-autonym="मराठी" data-language-local-name="马拉地语" class="interlanguage-link-target"><span>मराठी</span></a></li><li class="interlanguage-link interwiki-ms mw-list-item"><a href="https://ms.wikipedia.org/wiki/Teori_nombor" title="Teori nombor – 马来语" lang="ms" hreflang="ms" data-title="Teori nombor" data-language-autonym="Bahasa Melayu" data-language-local-name="马来语" class="interlanguage-link-target"><span>Bahasa Melayu</span></a></li><li class="interlanguage-link interwiki-mt mw-list-item"><a href="https://mt.wikipedia.org/wiki/Teorija_tan-numri" title="Teorija tan-numri – 马耳他语" lang="mt" hreflang="mt" data-title="Teorija tan-numri" data-language-autonym="Malti" data-language-local-name="马耳他语" class="interlanguage-link-target"><span>Malti</span></a></li><li class="interlanguage-link interwiki-my mw-list-item"><a href="https://my.wikipedia.org/wiki/%E1%80%80%E1%80%AD%E1%80%94%E1%80%BA%E1%80%B8%E1%80%9E%E1%80%AE%E1%80%A1%E1%80%AD%E1%80%AF%E1%80%9B%E1%80%AE" title="ကိန်းသီအိုရီ – 缅甸语" lang="my" hreflang="my" data-title="ကိန်းသီအိုရီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="缅甸语" class="interlanguage-link-target"><span>မြန်မာဘာသာ</span></a></li><li class="interlanguage-link interwiki-nds mw-list-item"><a href="https://nds.wikipedia.org/wiki/Tallentheorie" title="Tallentheorie – 低地德语" lang="nds" hreflang="nds" data-title="Tallentheorie" data-language-autonym="Plattdüütsch" data-language-local-name="低地德语" class="interlanguage-link-target"><span>Plattdüütsch</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Getaltheorie" title="Getaltheorie – 荷兰语" lang="nl" hreflang="nl" data-title="Getaltheorie" data-language-autonym="Nederlands" data-language-local-name="荷兰语" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-nn mw-list-item"><a href="https://nn.wikipedia.org/wiki/Talteori" title="Talteori – 挪威尼诺斯克语" lang="nn" hreflang="nn" data-title="Talteori" data-language-autonym="Norsk nynorsk" data-language-local-name="挪威尼诺斯克语" class="interlanguage-link-target"><span>Norsk nynorsk</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/Tallteori" title="Tallteori – 书面挪威语" lang="nb" hreflang="nb" data-title="Tallteori" data-language-autonym="Norsk bokmål" data-language-local-name="书面挪威语" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-oc mw-list-item"><a href="https://oc.wikipedia.org/wiki/Teoria_dels_nombres" title="Teoria dels nombres – 奥克语" lang="oc" hreflang="oc" data-title="Teoria dels nombres" data-language-autonym="Occitan" data-language-local-name="奥克语" class="interlanguage-link-target"><span>Occitan</span></a></li><li class="interlanguage-link interwiki-pa mw-list-item"><a href="https://pa.wikipedia.org/wiki/%E0%A8%85%E0%A9%B0%E0%A8%95_%E0%A8%B8%E0%A8%BF%E0%A8%A7%E0%A8%BE%E0%A8%82%E0%A8%A4" title="ਅੰਕ ਸਿਧਾਂਤ – 旁遮普语" lang="pa" hreflang="pa" data-title="ਅੰਕ ਸਿਧਾਂਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="旁遮普语" class="interlanguage-link-target"><span>ਪੰਜਾਬੀ</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Teoria_liczb" title="Teoria liczb – 波兰语" lang="pl" hreflang="pl" data-title="Teoria liczb" data-language-autonym="Polski" data-language-local-name="波兰语" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-pms mw-list-item"><a href="https://pms.wikipedia.org/wiki/Teor%C3%ACa_dij_n%C3%B9mer" title="Teorìa dij nùmer – 皮埃蒙特文" lang="pms" hreflang="pms" data-title="Teorìa dij nùmer" data-language-autonym="Piemontèis" data-language-local-name="皮埃蒙特文" class="interlanguage-link-target"><span>Piemontèis</span></a></li><li class="interlanguage-link interwiki-pnb mw-list-item"><a href="https://pnb.wikipedia.org/wiki/%D9%86%D9%85%D8%A8%D8%B1_%D8%AA%DA%BE%DB%8C%D9%88%D8%B1%DB%8C" title="نمبر تھیوری – Western Punjabi" lang="pnb" hreflang="pnb" data-title="نمبر تھیوری" data-language-autonym="پنجابی" data-language-local-name="Western Punjabi" class="interlanguage-link-target"><span>پنجابی</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/Teoria_dos_n%C3%BAmeros" title="Teoria dos números – 葡萄牙语" lang="pt" hreflang="pt" data-title="Teoria dos números" data-language-autonym="Português" data-language-local-name="葡萄牙语" class="interlanguage-link-target"><span>Português</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Teoria_numerelor" title="Teoria numerelor – 罗马尼亚语" lang="ro" hreflang="ro" data-title="Teoria numerelor" data-language-autonym="Română" data-language-local-name="罗马尼亚语" class="interlanguage-link-target"><span>Română</span></a></li><li class="interlanguage-link interwiki-ru mw-list-item"><a href="https://ru.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%8F_%D1%87%D0%B8%D1%81%D0%B5%D0%BB" title="Теория чисел – 俄语" lang="ru" hreflang="ru" data-title="Теория чисел" data-language-autonym="Русский" data-language-local-name="俄语" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sa mw-list-item"><a href="https://sa.wikipedia.org/wiki/%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE%E0%A4%B6%E0%A4%BE%E0%A4%B8%E0%A5%8D%E0%A4%A4%E0%A5%8D%E0%A4%B0%E0%A4%AE%E0%A5%8D" title="संख्याशास्त्रम् – 梵语" lang="sa" hreflang="sa" data-title="संख्याशास्त्रम्" data-language-autonym="संस्कृतम्" data-language-local-name="梵语" class="interlanguage-link-target"><span>संस्कृतम्</span></a></li><li class="interlanguage-link interwiki-sah mw-list-item"><a href="https://sah.wikipedia.org/wiki/%D0%A1%D0%B0%D0%B0%D0%BC%D0%B0%D0%B9_%D1%83%D0%BB%D0%B0%D1%85%D0%B0%D0%BD_%D1%83%D0%BE%D0%BF%D1%81%D0%B0%D0%B9_%D1%82%D2%AF%D2%A5%D1%8D%D1%82%D1%8D%D1%8D%D1%87%D1%87%D0%B8" title="Саамай улахан уопсай түҥэтээччи – 萨哈语" lang="sah" hreflang="sah" data-title="Саамай улахан уопсай түҥэтээччи" data-language-autonym="Саха тыла" data-language-local-name="萨哈语" class="interlanguage-link-target"><span>Саха тыла</span></a></li><li class="interlanguage-link interwiki-scn mw-list-item"><a href="https://scn.wikipedia.org/wiki/Tiur%C3%ACa_d%C3%AE_n%C3%B9mmura" title="Tiurìa dî nùmmura – 西西里语" lang="scn" hreflang="scn" data-title="Tiurìa dî nùmmura" data-language-autonym="Sicilianu" data-language-local-name="西西里语" class="interlanguage-link-target"><span>Sicilianu</span></a></li><li class="interlanguage-link interwiki-sco mw-list-item"><a href="https://sco.wikipedia.org/wiki/Nummer_theory" title="Nummer theory – 苏格兰语" lang="sco" hreflang="sco" data-title="Nummer theory" data-language-autonym="Scots" data-language-local-name="苏格兰语" class="interlanguage-link-target"><span>Scots</span></a></li><li class="interlanguage-link interwiki-sh mw-list-item"><a href="https://sh.wikipedia.org/wiki/Teorija_brojeva" title="Teorija brojeva – 塞尔维亚-克罗地亚语" lang="sh" hreflang="sh" data-title="Teorija brojeva" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="塞尔维亚-克罗地亚语" class="interlanguage-link-target"><span>Srpskohrvatski / српскохрватски</span></a></li><li class="interlanguage-link interwiki-simple mw-list-item"><a href="https://simple.wikipedia.org/wiki/Number_theory" title="Number theory – Simple English" lang="en-simple" hreflang="en-simple" data-title="Number theory" data-language-autonym="Simple English" data-language-local-name="Simple English" class="interlanguage-link-target"><span>Simple English</span></a></li><li class="interlanguage-link interwiki-sk mw-list-item"><a href="https://sk.wikipedia.org/wiki/Te%C3%B3ria_%C4%8D%C3%ADsel" title="Teória čísel – 斯洛伐克语" lang="sk" hreflang="sk" data-title="Teória čísel" data-language-autonym="Slovenčina" data-language-local-name="斯洛伐克语" class="interlanguage-link-target"><span>Slovenčina</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Teorija_%C5%A1tevil" title="Teorija števil – 斯洛文尼亚语" lang="sl" hreflang="sl" data-title="Teorija števil" data-language-autonym="Slovenščina" data-language-local-name="斯洛文尼亚语" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-sq mw-list-item"><a href="https://sq.wikipedia.org/wiki/Teoria_e_numrave" title="Teoria e numrave – 阿尔巴尼亚语" lang="sq" hreflang="sq" data-title="Teoria e numrave" data-language-autonym="Shqip" data-language-local-name="阿尔巴尼亚语" class="interlanguage-link-target"><span>Shqip</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D0%B8%D1%98%D0%B0_%D0%B1%D1%80%D0%BE%D1%98%D0%B5%D0%B2%D0%B0" title="Теорија бројева – 塞尔维亚语" lang="sr" hreflang="sr" data-title="Теорија бројева" data-language-autonym="Српски / srpski" data-language-local-name="塞尔维亚语" class="interlanguage-link-target"><span>Српски / srpski</span></a></li><li class="interlanguage-link interwiki-sv mw-list-item"><a href="https://sv.wikipedia.org/wiki/Talteori" title="Talteori – 瑞典语" lang="sv" hreflang="sv" data-title="Talteori" data-language-autonym="Svenska" data-language-local-name="瑞典语" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-sw mw-list-item"><a href="https://sw.wikipedia.org/wiki/Nadharia_ya_namba" title="Nadharia ya namba – 斯瓦希里语" lang="sw" hreflang="sw" data-title="Nadharia ya namba" data-language-autonym="Kiswahili" data-language-local-name="斯瓦希里语" class="interlanguage-link-target"><span>Kiswahili</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/%E0%AE%8E%E0%AE%A3%E0%AF%8D_%E0%AE%95%E0%AF%8B%E0%AE%9F%E0%AF%8D%E0%AE%AA%E0%AE%BE%E0%AE%9F%E0%AF%81" title="எண் கோட்பாடு – 泰米尔语" lang="ta" hreflang="ta" data-title="எண் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="泰米尔语" class="interlanguage-link-target"><span>தமிழ்</span></a></li><li class="interlanguage-link interwiki-th mw-list-item"><a href="https://th.wikipedia.org/wiki/%E0%B8%97%E0%B8%A4%E0%B8%A9%E0%B8%8E%E0%B8%B5%E0%B8%88%E0%B8%B3%E0%B8%99%E0%B8%A7%E0%B8%99" title="ทฤษฎีจำนวน – 泰语" lang="th" hreflang="th" data-title="ทฤษฎีจำนวน" data-language-autonym="ไทย" data-language-local-name="泰语" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tk mw-list-item"><a href="https://tk.wikipedia.org/wiki/Sanlar_teori%C3%BDasy" title="Sanlar teoriýasy – 土库曼语" lang="tk" hreflang="tk" data-title="Sanlar teoriýasy" data-language-autonym="Türkmençe" data-language-local-name="土库曼语" class="interlanguage-link-target"><span>Türkmençe</span></a></li><li class="interlanguage-link interwiki-tl mw-list-item"><a href="https://tl.wikipedia.org/wiki/Teorya_ng_bilang" title="Teorya ng bilang – 他加禄语" lang="tl" hreflang="tl" data-title="Teorya ng bilang" data-language-autonym="Tagalog" data-language-local-name="他加禄语" class="interlanguage-link-target"><span>Tagalog</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/Say%C4%B1lar_teorisi" title="Sayılar teorisi – 土耳其语" lang="tr" hreflang="tr" data-title="Sayılar teorisi" data-language-autonym="Türkçe" data-language-local-name="土耳其语" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-uk mw-list-item"><a href="https://uk.wikipedia.org/wiki/%D0%A2%D0%B5%D0%BE%D1%80%D1%96%D1%8F_%D1%87%D0%B8%D1%81%D0%B5%D0%BB" title="Теорія чисел – 乌克兰语" lang="uk" hreflang="uk" data-title="Теорія чисел" data-language-autonym="Українська" data-language-local-name="乌克兰语" class="interlanguage-link-target"><span>Українська</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/%D9%86%D8%B8%D8%B1%DB%8C%DB%82_%D8%B9%D8%AF%D8%AF" title="نظریۂ عدد – 乌尔都语" lang="ur" hreflang="ur" data-title="نظریۂ عدد" data-language-autonym="اردو" data-language-local-name="乌尔都语" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-uz mw-list-item"><a href="https://uz.wikipedia.org/wiki/Sonlar_nazariyasi" title="Sonlar nazariyasi – 乌兹别克语" lang="uz" hreflang="uz" data-title="Sonlar nazariyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="乌兹别克语" class="interlanguage-link-target"><span>Oʻzbekcha / ўзбекча</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/L%C3%BD_thuy%E1%BA%BFt_s%E1%BB%91" title="Lý thuyết số – 越南语" lang="vi" hreflang="vi" data-title="Lý thuyết số" data-language-autonym="Tiếng Việt" data-language-local-name="越南语" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-vo mw-list-item"><a href="https://vo.wikipedia.org/wiki/Numateor" title="Numateor – 沃拉普克语" lang="vo" hreflang="vo" data-title="Numateor" data-language-autonym="Volapük" data-language-local-name="沃拉普克语" class="interlanguage-link-target"><span>Volapük</span></a></li><li class="interlanguage-link interwiki-war mw-list-item"><a href="https://war.wikipedia.org/wiki/Teyorya_hin_ihap" title="Teyorya hin ihap – 瓦瑞语" lang="war" hreflang="war" data-title="Teyorya hin ihap" data-language-autonym="Winaray" data-language-local-name="瓦瑞语" class="interlanguage-link-target"><span>Winaray</span></a></li><li class="interlanguage-link interwiki-wuu mw-list-item"><a href="https://wuu.wikipedia.org/wiki/%E6%95%B0%E8%AE%BA" title="数论 – 吴语" lang="wuu" hreflang="wuu" data-title="数论" data-language-autonym="吴语" data-language-local-name="吴语" class="interlanguage-link-target"><span>吴语</span></a></li><li class="interlanguage-link interwiki-xmf mw-list-item"><a href="https://xmf.wikipedia.org/wiki/%E1%83%A0%E1%83%98%E1%83%AA%E1%83%AE%E1%83%A3%E1%83%94%E1%83%A4%E1%83%98%E1%83%A8_%E1%83%97%E1%83%94%E1%83%9D%E1%83%A0%E1%83%98%E1%83%90" title="რიცხუეფიშ თეორია – 明格列爾文" lang="xmf" hreflang="xmf" data-title="რიცხუეფიშ თეორია" data-language-autonym="მარგალური" data-language-local-name="明格列爾文" class="interlanguage-link-target"><span>მარგალური</span></a></li><li class="interlanguage-link interwiki-yi mw-list-item"><a href="https://yi.wikipedia.org/wiki/%D7%A0%D7%95%D7%9E%D7%A2%D7%A8%D7%9F_%D7%98%D7%A2%D7%90%D7%A8%D7%99%D7%A2" title="נומערן טעאריע – 意第绪语" lang="yi" hreflang="yi" data-title="נומערן טעאריע" data-language-autonym="ייִדיש" data-language-local-name="意第绪语" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh-min-nan mw-list-item"><a href="https://zh-min-nan.wikipedia.org/wiki/S%C3%B2%CD%98-l%C5%ABn" title="Sò͘-lūn – 闽南语" lang="nan" hreflang="nan" data-title="Sò͘-lūn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="闽南语" class="interlanguage-link-target"><span>閩南語 / Bân-lâm-gú</span></a></li><li class="interlanguage-link interwiki-zh-yue mw-list-item"><a href="https://zh-yue.wikipedia.org/wiki/%E6%95%B8%E8%AB%96" title="數論 – 粤语" lang="yue" hreflang="yue" data-title="數論" data-language-autonym="粵語" data-language-local-name="粤语" class="interlanguage-link-target"><span>粵語</span></a></li> </ul> <div class="after-portlet after-portlet-lang"><span class="wb-langlinks-edit wb-langlinks-link"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q12479#sitelinks-wikipedia" title="编辑跨语言链接" class="wbc-editpage">编辑链接</a></span></div> </div> </div> </div> </header> <div class="vector-page-toolbar"> <div class="vector-page-toolbar-container"> <div id="left-navigation"> <nav aria-label="命名空间"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/%E6%95%B0%E8%AE%BA" title="浏览条目正文[c]" accesskey="c"><span>条目</span></a></li><li id="ca-talk" 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.ambox-content{border-left-color:#f28500!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-style{border-left-color:#fc3!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-move{border-left-color:#9932cc!important}html.skin-theme-clientpref-os .mw-parser-output .ambox-protection{border-left-color:#a2a9b1!important}}</style><table class="box-问题条目 plainlinks metadata ambox ambox-content ambox-multiple_issues compact-ambox" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/40px-Ambox_important.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/60px-Ambox_important.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/b/b4/Ambox_important.svg/80px-Ambox_important.svg.png 2x" data-file-width="40" data-file-height="40" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span"><div class="multiple-issues-text mw-collapsible"><b>本條目存在以下問題</b>，請協助<b><a class="external text" href="https://zh.wikipedia.org/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit">改善本條目</a></b>或在<b><a href="/wiki/Talk:%E6%95%B0%E8%AE%BA" title="Talk:数论">討論頁</a></b>針對議題發表看法。 <div class="mw-collapsible-content"> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r83732972"><table class="box-Lead_too_short plainlinks metadata ambox ambox-content ambox-lead_too_short" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span typeof="mw:File"><a href="/wiki/File:Wiki_letter_w.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/40px-Wiki_letter_w.svg.png" decoding="async" width="40" height="40" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/60px-Wiki_letter_w.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/6/6c/Wiki_letter_w.svg/80px-Wiki_letter_w.svg.png 2x" data-file-width="44" data-file-height="44" /></a></span></div></td><td class="mbox-text"><div class="mbox-text-span">此条目<b><a href="/wiki/Wikipedia:%E6%A0%BC%E5%BC%8F%E6%89%8B%E5%86%8A/%E5%BA%8F%E8%A8%80%E7%AB%A0%E7%AF%80" title="Wikipedia:格式手冊/序言章節">序言章节</a>没有充分<a href="/wiki/Wikipedia:%E6%91%98%E8%A6%81%E6%A0%BC%E5%BC%8F" title="Wikipedia:摘要格式">总结</a>全文内容要点</b>。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2022年4月12日</span>)</i></small><span class="hide-when-compact"><br /><small>请考虑扩充序言，<a href="/wiki/Wikipedia:%E6%A0%BC%E5%BC%8F%E6%89%8B%E5%86%8A/%E5%BA%8F%E8%A8%80%E7%AB%A0%E7%AF%80#提供易讀的總覽" title="Wikipedia:格式手冊/序言章節">清晰概述</a>条目所有重點。请在条目的<a href="/wiki/Talk:%E6%95%B0%E8%AE%BA" title="Talk:数论">讨论页</a>讨论此问题。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r83732972"><table class="box-Expand_language plainlinks metadata ambox ambox-notice" role="presentation"><tbody><tr><td class="mbox-image"><div style="width:52px"><span class="skin-invert" typeof="mw:File"><span><img alt="" src="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/50px-Translation_to_zh_arrow.svg.png" decoding="async" width="50" height="17" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/75px-Translation_to_zh_arrow.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/da/Translation_to_zh_arrow.svg/100px-Translation_to_zh_arrow.svg.png 2x" data-file-width="60" data-file-height="20" /></span></span></div></td><td class="mbox-text"><div class="mbox-text-span">此條目<b>可参照<a href="https://en.wikipedia.org/wiki/Number_theory" class="extiw" title="en:Number theory">英語維基百科</a>相應條目来扩充</b>。<span class="hide-when-compact"></span> <small class="date-container"><i>(<span class="date">2022年4月12日</span>)</i></small><span class="hide-when-compact"><br /><small>若您熟悉来源语言和主题，请协助<a href="/wiki/Wikipedia:%E7%BF%BB%E8%AF%91%E5%AE%88%E5%88%99" class="mw-redirect" title="Wikipedia:翻译守则">参考外语维基百科扩充条目</a>。请勿直接提交机械翻译，也不要翻译不可靠、低品质内容。依<a href="/wiki/Wikipedia:%E5%9C%A8%E7%BB%B4%E5%9F%BA%E7%99%BE%E7%A7%91%E5%86%85%E5%A4%8D%E5%88%B6%E5%86%85%E5%AE%B9" title="Wikipedia:在维基百科内复制内容">版权协议</a>，译文需<a href="/wiki/Wikipedia:%E7%B7%A8%E8%BC%AF%E6%91%98%E8%A6%81#翻譯文章" title="Wikipedia:編輯摘要">在编辑摘要注明来源</a>，或于讨论页顶部标记<code>{{<a href="/wiki/Template:Translated_page" title="Template:Translated page">Translated page</a>}}</code>标签。</small></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> </div></div><span class="hide-when-compact"></span><span class="hide-when-compact"></span></div></td></tr></tbody></table> <style 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class="sidebar-content-with-subgroup"> <table class="sidebar-subgroup"><tbody><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-top:1px solid #aaa;background:#ddddff;text-align:center;"><a href="/wiki/%E6%95%B0%E5%AD%A6%E9%A2%86%E5%9F%9F" title="数学领域">领域</a></div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a class="mw-selflink selflink">数论</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95%E5%AD%A6" title="几何学">几何学</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B0" title="代数">代数</a></li> <li><a href="/wiki/%E5%BE%AE%E7%A7%AF%E5%88%86%E5%AD%A6" title="微积分学">微积分</a>与<a href="/wiki/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90" title="数学分析">分析学</a></li> <li><a href="/wiki/%E7%A6%BB%E6%95%A3%E6%95%B0%E5%AD%A6" title="离散数学">离散数学</a></li> <li><a href="/wiki/%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91" title="数理逻辑">逻辑学</a>与<a href="/wiki/%E9%9B%86%E5%90%88%E8%AE%BA" title="集合论">集合论</a></li> <li><a href="/wiki/%E6%A6%82%E7%8E%87" title="概率">概率</a></li> <li><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6" title="统计学">统计学</a>与<a href="/wiki/%E5%86%B3%E7%AD%96%E8%AE%BA" title="决策论">决策论</a></li></ul></div></div></td> </tr><tr><td class="sidebar-content"> <div class="sidebar-list mw-collapsible"><div class="sidebar-list-title" style="border-top:1px solid #aaa;background:#ddddff;text-align:center;">与其他科学的关系</div><div class="sidebar-list-content mw-collapsible-content hlist"> <ul><li><a href="/wiki/%E6%95%B0%E5%AD%A6%E7%89%A9%E7%90%86" title="数学物理">物理学</a></li> <li><a href="/wiki/%E8%BF%90%E7%AE%97%E6%95%B0%E5%AD%A6" title="运算数学">运算学</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%94%9F%E7%89%A9%E5%AD%B8" title="數理生物學">生物学</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E8%AF%AD%E8%A8%80%E5%AD%A6" title="计算语言学">语言学</a></li> <li><a href="/wiki/%E6%95%B0%E7%90%86%E7%BB%8F%E6%B5%8E%E5%AD%A6" title="数理经济学">经济学</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%93%B2%E5%AD%A6" title="数学哲学">哲学</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E6%95%99%E8%82%B2" title="数学教育">教育学</a></li></ul></div></div></td> </tr></tbody></table></td> </tr><tr><th class="sidebar-heading"> <span typeof="mw:File"><span title="主题"><img alt="主题" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <a href="/wiki/Portal:%E6%95%B0%E5%AD%A6" title="Portal:数学">数学主题</a></th></tr><tr><td class="sidebar-navbar" style="line-height:1.6"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84244141">.mw-parser-output .navbar{display:inline;font-weight:normal}.mw-parser-output .navbar-collapse{float:left;text-align:left}.mw-parser-output .navbar-boxtext{word-spacing:0}.mw-parser-output .navbar ul{display:inline-block;white-space:nowrap;line-height:inherit}.mw-parser-output .navbar-brackets::before{margin-right:-0.125em;content:"[ "}.mw-parser-output .navbar-brackets::after{margin-left:-0.125em;content:" ]"}.mw-parser-output .navbar li{word-spacing:-0.125em}.mw-parser-output .navbar a>span,.mw-parser-output .navbar a>abbr{text-decoration:inherit}.mw-parser-output .navbar-mini abbr{font-variant:small-caps;border-bottom:none;text-decoration:none;cursor:inherit}.mw-parser-output .navbar-ct-full{font-size:110%;margin:0 8em}.mw-parser-output .navbar-ct-mini{font-size:110%;margin:0 5em}html.skin-theme-clientpref-night .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}@media(prefers-color-scheme:dark){html.skin-theme-clientpref-os .mw-parser-output .navbar li a abbr{color:var(--color-base)!important}}@media print{.mw-parser-output .navbar{display:none!important}}</style><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%95%B0%E5%AD%A6%E8%AF%9D%E9%A2%98%E4%BE%A7%E8%BE%B9%E6%A0%8F" title="Template:数学话题侧边栏"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E6%95%B0%E5%AD%A6%E8%AF%9D%E9%A2%98%E4%BE%A7%E8%BE%B9%E6%A0%8F" title="Template talk:数学话题侧边栏"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E6%95%B0%E5%AD%A6%E8%AF%9D%E9%A2%98%E4%BE%A7%E8%BE%B9%E6%A0%8F" title="Special:编辑页面/Template:数学话题侧边栏"><abbr title="编辑该模板">编</abbr></a></li></ul></div></td></tr></tbody></table> <p><b>數論</b>（英語：<span lang="en">Number theory</span>）是<a href="/wiki/%E7%BA%AF%E7%B2%B9%E6%95%B0%E5%AD%A6" class="mw-redirect" title="纯粹数学">纯粹数学</a>的分支之一，主要研究<a href="/wiki/%E6%95%B4%E6%95%B0" title="整数">整数</a>的性質，被稱為「最純」的數學領域。 </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="简介"><span id=".E7.AE.80.E4.BB.8B"></span>简介</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=1" title="编辑章节：简介"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r61209892">.mw-parser-output .templatequote{margin-top:0;overflow:hidden}.mw-parser-output .templatequote .templatequotecite{line-height:1em;text-align:left;padding-left:2em;margin-top:0}.mw-parser-output .templatequote .templatequotecite cite{font-size:small}</style> <blockquote class="templatequote"><p>數學是科學的皇后，數論是數學的皇后。<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup><span id="noteTag-cite_ref-sup"><sup id="cite_ref-2" class="reference"><a href="#cite_note-2"><span class="cite-bracket">[</span>註 1<span class="cite-bracket">]</span></a></sup></span><br /> ——<a href="/wiki/%E5%8D%A1%E5%B0%94%C2%B7%E5%BC%97%E9%87%8C%E5%BE%B7%E9%87%8C%E5%B8%8C%C2%B7%E9%AB%98%E6%96%AF" class="mw-redirect" title="卡尔·弗里德里希·高斯">卡尔·弗里德里希·高斯</a></p></blockquote> <p>正整数按乘法性质划分，可以分成<a href="/wiki/%E8%B3%AA%E6%95%B8" class="mw-redirect" title="質數">質数</a>，<a href="/wiki/%E5%90%88%E6%95%B0" title="合数">合数</a>，<a href="/wiki/1" title="1">1</a>，質数產生了很多一般人能理解卻又懸而未解的問題，如<a href="/wiki/%E5%93%A5%E5%BE%B7%E5%B7%B4%E8%B5%AB%E7%8C%9C%E6%83%B3" title="哥德巴赫猜想">哥德巴赫猜想</a>，<a href="/wiki/%E5%AD%AA%E7%94%9F%E8%B4%A8%E6%95%B0%E7%8C%9C%E6%83%B3" class="mw-redirect" title="孪生质数猜想">孿生質數猜想</a>等。即，很多問題虽然形式上十分初等，事实上却要用到许多艰深的数学知识。这一领域的研究从某种意义上推动了数学的发展，催生了大量的新思想和新方法。數論除了研究整數及質數外，也研究一些由整數衍生的數（如<a href="/wiki/%E6%9C%89%E7%90%86%E6%95%B8" class="mw-redirect" title="有理數">有理數</a>）或是一些廣義的整數（如<a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B4%E6%95%B8" title="代數整數">代數整數</a>）。 </p><p>整数可以是方程式的解（<a href="/wiki/%E4%B8%9F%E7%95%AA%E5%9C%96%E6%96%B9%E7%A8%8B" title="丟番圖方程">丟番圖方程</a>）。有些<a href="/wiki/%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B8" class="mw-redirect" title="解析函數">解析函數</a>（像<a href="/wiki/%E9%BB%8E%E6%9B%BC%CE%B6%E5%87%BD%E6%95%B8" title="黎曼ζ函數">黎曼ζ函數</a>）中包括了一些整數、質數的性質，透過這些函數也可以了解一些數論的問題。透過數論也可以建立實數和有理數之間的關係，並且用有理數來逼近實數（<a href="/wiki/%E4%B8%9F%E7%95%AA%E5%9C%96%E9%80%BC%E8%BF%91" title="丟番圖逼近">丟番圖逼近</a>）。 </p> <div class="mw-heading mw-heading2"><h2 id="历史"><span id=".E5.8E.86.E5.8F.B2"></span>历史</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=2" title="编辑章节：历史"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="古代"><span id=".E5.8F.A4.E4.BB.A3"></span>古代</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=3" title="编辑章节：古代"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>數論早期也稱為<a href="/wiki/%E7%AE%97%E8%A1%93" class="mw-redirect" title="算術">算術</a><span id="noteTag-cite_ref-sup"><sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>註 2<span class="cite-bracket">]</span></a></sup></span>，而<a href="/wiki/%E7%AE%97%E8%A1%93" class="mw-redirect" title="算術">算術</a>一詞則表示「基本運算」<span id="noteTag-cite_ref-sup"><sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>註 3<span class="cite-bracket">]</span></a></sup></span><sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup>，在现代数论诞生前，早期铺垫有三大内容： </p> <ol><li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97" title="欧几里得">欧几里得</a>证明<a href="/wiki/%E7%B4%A0%E6%95%B0" class="mw-redirect" title="素数">质数</a>无穷多。</li> <li>寻找<a href="/wiki/%E7%B4%A0%E6%95%B0" class="mw-redirect" title="素数">质数</a>的<a href="/wiki/%E5%9F%83%E6%8B%89%E6%89%98%E6%96%AF%E7%89%B9%E5%B0%BC%E7%AD%9B%E6%B3%95" title="埃拉托斯特尼筛法">埃拉托斯特尼筛法</a>；欧几里得求最大公约数的<a href="/wiki/%E8%BE%97%E8%BD%AC%E7%9B%B8%E9%99%A4%E6%B3%95" class="mw-redirect" title="辗转相除法">辗转相除法</a>。</li> <li>公元420至589年（中国南北朝时期）的<a href="/wiki/%E5%AD%99%E5%AD%90%E5%AE%9A%E7%90%86" class="mw-redirect" title="孙子定理">孙子定理</a>。</li></ol> <div class="mw-heading mw-heading3"><h3 id="中世纪"><span id=".E4.B8.AD.E4.B8.96.E7.BA.AA"></span>中世纪</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=4" title="编辑章节：中世纪"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>在中世紀早期，除了1175年至1200年住在<a href="/wiki/%E5%8C%97%E9%9D%9E" title="北非">北非</a>和<a href="/wiki/%E5%90%9B%E5%A3%AB%E5%9D%A6%E4%B8%81%E5%A0%A1" title="君士坦丁堡">君士坦丁堡</a>的数学家<a href="/wiki/%E6%96%90%E6%B3%A2%E9%82%A3%E5%A5%91" title="斐波那契">斐波那契</a>有關<a href="/wiki/%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97" title="等差数列">等差数列</a>的研究外，<a href="/wiki/%E8%A5%BF%E6%AC%A7" title="西欧">西欧</a>在數論上沒有什麼進展。 </p><p>中世纪数论主要是指15-16世纪由<a href="/wiki/%E8%B4%B9%E9%A9%AC" class="mw-redirect" title="费马">费马</a>、<a href="/wiki/%E9%A6%AC%E8%98%AD%C2%B7%E6%A2%85%E6%A3%AE" class="mw-redirect" title="馬蘭·梅森">梅森</a>、<a href="/wiki/%E6%AC%A7%E6%8B%89" class="mw-redirect" title="欧拉">欧拉</a>、<a href="/wiki/%E9%AB%98%E6%96%AF" class="mw-redirect" title="高斯">高斯</a>、<a href="/wiki/%E5%8B%92%E8%AE%93%E5%BE%B7" class="mw-redirect" title="勒讓德">勒让德</a>、<a href="/wiki/%E9%BB%8E%E6%9B%BC" class="mw-redirect" title="黎曼">黎曼</a>、<a href="/wiki/%E5%B8%8C%E5%B0%94%E4%BC%AF%E7%89%B9" class="mw-redirect" title="希尔伯特">希尔伯特</a>等人发展的数论。最早是在<a href="/wiki/%E6%96%87%E8%97%9D%E5%BE%A9%E8%88%88" class="mw-redirect" title="文藝復興">文藝復興</a>的末期，對於<a href="/wiki/%E5%8F%A4%E5%B8%8C%E8%87%98" class="mw-redirect" title="古希臘">古希臘</a>著作的重新研究。主要的成因是因為<a href="/wiki/%E4%B8%A2%E7%95%AA%E5%9B%BE" title="丢番图">丟番圖</a>的《算術》（Arithmetica）一書的校正及翻譯為<a href="/wiki/%E6%8B%89%E4%B8%81%E6%96%87" class="mw-redirect" title="拉丁文">拉丁文</a>，早在1575年Xylander曾試圖翻譯，但不成功，後來才由Bachet在1621年翻譯完成。 </p> <div class="mw-heading mw-heading3"><h3 id="近代"><span id=".E8.BF.91.E4.BB.A3"></span>近代</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=5" title="编辑章节：近代"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="費馬"><span id=".E8.B2.BB.E9.A6.AC"></span>費馬</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=6" title="编辑章节：費馬"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size mw-halign-right" typeof="mw:File/Thumb"><a href="/wiki/File:Pierre_de_Fermat.png" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Pierre_de_Fermat.png/170px-Pierre_de_Fermat.png" decoding="async" width="170" height="301" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Pierre_de_Fermat.png/255px-Pierre_de_Fermat.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4b/Pierre_de_Fermat.png/340px-Pierre_de_Fermat.png 2x" data-file-width="566" data-file-height="1003" /></a><figcaption>費馬</figcaption></figure> <p><a href="/wiki/%E7%9A%AE%E5%9F%83%E7%88%BE%C2%B7%E5%BE%B7%C2%B7%E8%B2%BB%E9%A6%AC" title="皮埃爾·德·費馬">皮埃爾·德·費馬</a>（1601–1665）沒有著作出版，他在數論上的貢獻幾乎都在他寫給其他數學家的信上，以及書旁的空白處<sup id="cite_ref-FOOTNOTEWeil198445–46_7-0" class="reference"><a href="#cite_note-FOOTNOTEWeil198445–46-7"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup>。費馬的貢獻幾乎沒有數論上的證明<sup id="cite_ref-8" class="reference"><a href="#cite_note-8"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup>，不過費馬重覆的使用<a href="/wiki/%E6%95%B8%E5%AD%B8%E6%AD%B8%E7%B4%8D%E6%B3%95" class="mw-redirect" title="數學歸納法">數學歸納法</a>，並引入<a href="/wiki/%E6%97%A0%E7%A9%B7%E9%80%92%E9%99%8D%E6%B3%95" title="无穷递降法">无穷递降法</a>。 </p><p>費馬最早的興趣是在<a href="/wiki/%E5%AE%8C%E5%85%A8%E6%95%B8" class="mw-redirect" title="完全數">完全數</a>及<a href="/wiki/%E7%9B%B8%E4%BA%B2%E6%95%B0" title="相亲数">相亲数</a>，因此開始研究整數<a href="/wiki/%E5%9B%A0%E6%95%B8" title="因數">因數</a>，這也開始1636年之後的數學研究，也接觸到當時的數學社群<sup id="cite_ref-9" class="reference"><a href="#cite_note-9"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup>。他已在1643年研讀過<span class="ilh-all" data-orig-title="克劳德-加斯帕·巴歇·德·梅齐里亚克" data-lang-code="en" data-lang-name="英语" data-foreign-title="Claude Gaspard Bachet de Méziriac"><span class="ilh-page"><a href="/w/index.php?title=%E5%85%8B%E5%8A%B3%E5%BE%B7-%E5%8A%A0%E6%96%AF%E5%B8%95%C2%B7%E5%B7%B4%E6%AD%87%C2%B7%E5%BE%B7%C2%B7%E6%A2%85%E9%BD%90%E9%87%8C%E4%BA%9A%E5%85%8B&action=edit&redlink=1" class="new" title="克劳德-加斯帕·巴歇·德·梅齐里亚克（页面不存在）">巴歇</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Claude_Gaspard_Bachet_de_M%C3%A9ziriac" class="extiw" title="en:Claude Gaspard Bachet de Méziriac"><span lang="en" dir="auto">Claude Gaspard Bachet de Méziriac</span></a></span>）</span></span>版本的丟番圖著作，他的興趣開始轉向<a href="/wiki/%E4%B8%9F%E7%95%AA%E5%9C%96%E6%96%B9%E7%A8%8B" title="丟番圖方程">丟番圖方程</a>和<a href="/wiki/%E5%B9%B3%E6%96%B9%E6%95%B8" class="mw-redirect" title="平方數">平方數</a>的和<sup id="cite_ref-FOOTNOTEWeil198453_10-0" class="reference"><a href="#cite_note-FOOTNOTEWeil198453-10"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup>。 </p><p>費馬在數論上的貢獻有： </p> <ul><li><a href="/wiki/%E8%B2%BB%E9%A6%AC%E5%B0%8F%E5%AE%9A%E7%90%86" class="mw-redirect" title="費馬小定理">費馬小定理</a> (1640)<sup id="cite_ref-11" class="reference"><a href="#cite_note-11"><span class="cite-bracket">[</span>8<span class="cite-bracket">]</span></a></sup>，若<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span>不是質數<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/81eac1e205430d1f40810df36a0edffdc367af36" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:1.259ex; height:2.009ex;" alt="{\displaystyle p}"></span>的倍數，則<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{p-1}\equiv 1{\pmod {p}}.}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>p</mi> <mo>−</mo> <mn>1</mn> </mrow> </msup> <mo>≡</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <mi>p</mi> <mo stretchy="false">)</mo> </mrow> <mo>.</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{p-1}\equiv 1{\pmod {p}}.}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/58a9e1a77254c598a3bbd20ee75962c540381c54" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:20.151ex; height:3.176ex;" alt="{\displaystyle a^{p-1}\equiv 1{\pmod {p}}.}"></span></li> <li>若<i><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ffd2487510aa438433a2579450ab2b3d557e5edc" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.23ex; height:1.676ex;" alt="{\displaystyle a}"></span></i>和<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle b}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>b</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle b}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f11423fbb2e967f986e36804a8ae4271734917c3" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:0.998ex; height:2.176ex;" alt="{\displaystyle b}"></span><a href="/wiki/%E4%BA%92%E8%B3%AA" title="互質">互質</a>，則<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}+b^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}+b^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14fc28103c5d2aa9276728469f82c9f415f4b257" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.176ex; height:2.843ex;" alt="{\displaystyle a^{2}+b^{2}}"></span>無法被任何除4後同餘-1的質數整除<sup id="cite_ref-12" class="reference"><a href="#cite_note-12"><span class="cite-bracket">[</span>9<span class="cite-bracket">]</span></a></sup>，而且每個除4後同餘1的質數都可以表示為<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle a^{2}+b^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>a</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>b</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}+b^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/14fc28103c5d2aa9276728469f82c9f415f4b257" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.176ex; height:2.843ex;" alt="{\displaystyle a^{2}+b^{2}}"></span>.<sup id="cite_ref-FOOTNOTETanneryHenry1891Vol._II,_p._213_13-0" class="reference"><a href="#cite_note-FOOTNOTETanneryHenry1891Vol._II,_p._213-13"><span class="cite-bracket">[</span>10<span class="cite-bracket">]</span></a></sup>，這二個是在1640年證明的，在1649年他在寫給<a href="/wiki/%E6%83%A0%E6%9B%B4%E6%96%AF" class="mw-redirect" title="惠更斯">惠更斯</a>的信上提到他用<a href="/wiki/%E6%97%A0%E7%A9%B7%E9%80%92%E9%99%8D%E6%B3%95" title="无穷递降法">无穷递降法</a>證明的第二個問題<sup id="cite_ref-FOOTNOTETanneryHenry1891Vol._II,_p._423_14-0" class="reference"><a href="#cite_note-FOOTNOTETanneryHenry1891Vol._II,_p._423-14"><span class="cite-bracket">[</span>11<span class="cite-bracket">]</span></a></sup>，費馬和<span class="ilh-all" data-orig-title="福蘭尼可" data-lang-code="en" data-lang-name="英语" data-foreign-title="Frenicle"><span class="ilh-page"><a href="/w/index.php?title=%E7%A6%8F%E8%98%AD%E5%B0%BC%E5%8F%AF&action=edit&redlink=1" class="new" title="福蘭尼可（页面不存在）">福蘭尼可</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Frenicle" class="extiw" title="en:Frenicle"><span lang="en" dir="auto">Frenicle</span></a></span>）</span></span>在其他平方形式上也有一些貢獻，不過其中有些錯誤及不嚴謹之處<sup id="cite_ref-FOOTNOTEWeil198480,_91–92_15-0" class="reference"><a href="#cite_note-FOOTNOTEWeil198480,_91–92-15"><span class="cite-bracket">[</span>12<span class="cite-bracket">]</span></a></sup>。</li> <li>向英國的數學家提出了求解<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}-Ny^{2}=1}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mi>N</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}-Ny^{2}=1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0fa2a18557e1553bfe01d2ed1dfeafed52b42c02" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.764ex; height:3.009ex;" alt="{\displaystyle x^{2}-Ny^{2}=1}"></span>的挑戰（1657年），但在幾個月後就由Wallis及Brouncker證明<sup id="cite_ref-FOOTNOTEWeil198492_16-0" class="reference"><a href="#cite_note-FOOTNOTEWeil198492-16"><span class="cite-bracket">[</span>13<span class="cite-bracket">]</span></a></sup>。費馬認為他們的證明有效，但用了一個在其中未經證明的演算法，費馬自己是由无穷递降法找到證明。</li> <li>發展許多找<a href="/wiki/%E4%BA%8F%E6%A0%BC" title="亏格">亏格</a>0或1曲線上點的方法，作法類似丟番圖，有許多特殊的步驟，使用了<a href="/wiki/%E5%88%87%E7%BA%BF%E6%B3%95" title="切线法">切線法</a>構建曲線，而不是用<a href="/wiki/%E5%89%B2%E7%BA%BF%E6%B3%95" title="割线法">割線法</a><sup id="cite_ref-FOOTNOTEWeil1984Ch._II,_sect._XV_and_XVI_17-0" class="reference"><a href="#cite_note-FOOTNOTEWeil1984Ch._II,_sect._XV_and_XVI-17"><span class="cite-bracket">[</span>14<span class="cite-bracket">]</span></a></sup>。</li> <li>證明<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{4}+y^{4}=z^{4}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{4}+y^{4}=z^{4}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bfc85e410302961db48dfb90dfb4f27372961922" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.682ex; height:3.009ex;" alt="{\displaystyle x^{4}+y^{4}=z^{4}}"></span>不存在非尋常的正整數解。</li></ul> <p>費馬在1637年聲稱（<a href="/wiki/%E8%B2%BB%E9%A6%AC%E6%9C%80%E5%BE%8C%E5%AE%9A%E7%90%86" class="mw-redirect" title="費馬最後定理">費馬最後定理</a>）證明了對於大於2的任意整數<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a601995d55609f2d9f5e233e36fbe9ea26011b3b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.395ex; height:1.676ex;" alt="{\displaystyle n}"></span>，不存在 <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{n}+y^{n}=z^{n}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> <mo>=</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mi>n</mi> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{n}+y^{n}=z^{n}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c34dcc46ebfb58e1b91a6c0caa1470e76139543a" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:13.175ex; height:2.676ex;" alt="{\displaystyle x^{n}+y^{n}=z^{n}}"></span>的非尋常的正整數解（目前已知唯一的证明是由數學家<a href="/wiki/%E5%AE%89%E5%BE%B7%E9%AD%AF%C2%B7%E6%87%B7%E7%88%BE%E6%96%AF" title="安德魯·懷爾斯">安德魯·懷爾斯</a>及其學生<a href="/wiki/%E7%90%86%E6%9F%A5%C2%B7%E6%B3%B0%E5%8B%92_(%E6%95%B8%E5%AD%B8%E5%AE%B6)" class="mw-redirect" title="理查·泰勒 (數學家)">理查·泰勒</a>于1994年完成的證明），但只在一本丟番圖著作的旁邊寫到，而且他沒有向別人宣稱他已有了證明<sup id="cite_ref-FOOTNOTEWeil1984104_18-0" class="reference"><a href="#cite_note-FOOTNOTEWeil1984104-18"><span class="cite-bracket">[</span>15<span class="cite-bracket">]</span></a></sup>。 </p> <div class="mw-heading mw-heading4"><h4 id="歐拉"><span id=".E6.AD.90.E6.8B.89"></span>歐拉</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=7" title="编辑章节：歐拉"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="/wiki/File:Leonhard_Euler.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Leonhard_Euler.jpg/170px-Leonhard_Euler.jpg" decoding="async" width="170" height="220" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Leonhard_Euler.jpg/255px-Leonhard_Euler.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/d/d7/Leonhard_Euler.jpg/340px-Leonhard_Euler.jpg 2x" data-file-width="4672" data-file-height="6040" /></a><figcaption>歐拉</figcaption></figure> <p><a href="/wiki/%E6%AD%90%E6%8B%89" class="mw-redirect" title="歐拉">歐拉</a>(1707–1783)對數論的興趣最早是由他的朋友<a href="/wiki/%E5%85%8B%E9%87%8C%E6%96%AF%E8%92%82%E5%AE%89%C2%B7%E5%93%A5%E5%BE%B7%E5%B7%B4%E8%B5%AB" title="克里斯蒂安·哥德巴赫">哥德巴赫</a>所引發，讓他開始專注在<a href="/wiki/%E8%B2%BB%E9%A6%AC" class="mw-redirect" title="費馬">費馬</a>的一些研究上<sup id="cite_ref-FOOTNOTEWeil19842,_172_19-0" class="reference"><a href="#cite_note-FOOTNOTEWeil19842,_172-19"><span class="cite-bracket">[</span>16<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEVaradarajan20069_20-0" class="reference"><a href="#cite_note-FOOTNOTEVaradarajan20069-20"><span class="cite-bracket">[</span>17<span class="cite-bracket">]</span></a></sup>，在費馬沒有使當代的數學家注意此一主題後，歐拉的出現稱為「現代數論的重生」<sup id="cite_ref-21" class="reference"><a href="#cite_note-21"><span class="cite-bracket">[</span>18<span class="cite-bracket">]</span></a></sup>。歐拉數論的貢獻包括以下幾項<sup id="cite_ref-22" class="reference"><a href="#cite_note-22"><span class="cite-bracket">[</span>19<span class="cite-bracket">]</span></a></sup>： </p> <ul><li>費馬研究的證明，包括<a href="/wiki/%E8%B2%BB%E9%A6%AC%E5%B0%8F%E5%AE%9A%E7%90%86" class="mw-redirect" title="費馬小定理">費馬小定理</a>（歐拉延伸到非質數的模數），以及<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p=x^{2}+y^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>=</mo> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p=x^{2}+y^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fe433e9ba9c42efe1bc9fd51bb439c698b8f6843" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:11.796ex; height:3.009ex;" alt="{\displaystyle p=x^{2}+y^{2}}"></span><a href="/wiki/%E8%8B%A5%E4%B8%94%E5%94%AF%E8%8B%A5" class="mw-redirect" title="若且唯若">若且唯若</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle p\equiv 1\;mod\;4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>p</mi> <mo>≡</mo> <mn>1</mn> <mspace width="thickmathspace" /> <mi>m</mi> <mi>o</mi> <mi>d</mi> <mspace width="thickmathspace" /> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle p\equiv 1\;mod\;4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/47246d58f9dcb2e7f8b1dce532e52271db9d1fe1" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; margin-left: -0.089ex; width:12.356ex; height:2.509ex;" alt="{\displaystyle p\equiv 1\;mod\;4}"></span>，這項研究可推導到所有整數都可以表示為四個平方數的證明（第一個完整證明是由<a href="/wiki/%E7%B4%84%E7%91%9F%E5%A4%AB%C2%B7%E6%8B%89%E6%A0%BC%E6%9C%97%E6%97%A5" class="mw-redirect" title="約瑟夫·拉格朗日">約瑟夫·拉格朗日</a>提出，費馬很快的也提出證明），和<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{4}+y^{4}=z^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>+</mo> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> <mo>=</mo> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{4}+y^{4}=z^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/f35aa613c26db550f2733d251ae8cbcb906831ec" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:12.682ex; height:3.009ex;" alt="{\displaystyle x^{4}+y^{4}=z^{2}}"></span>沒有非零整數解的證明，表示為<a href="/wiki/%E8%B2%BB%E9%A6%AC%E6%9C%80%E5%BE%8C%E5%AE%9A%E7%90%86" class="mw-redirect" title="費馬最後定理">費馬最後定理</a><span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=4}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>4</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=4}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/d928ec15aeef83aade867992ee473933adb6139d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=4}"></span>時成立，歐拉用類似方式證明了<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n=3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>=</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n=3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/1c5a5a42ced00df920fad4ab2d4acdb960a4105b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:5.656ex; height:2.176ex;" alt="{\displaystyle n=3}"></span>的情形。</li> <li><a href="/wiki/%E4%BD%A9%E5%B0%94%E6%96%B9%E7%A8%8B" title="佩尔方程">佩爾方程</a>，最早誤以為是歐拉證明<sup id="cite_ref-Eulpell_23-0" class="reference"><a href="#cite_note-Eulpell-23"><span class="cite-bracket">[</span>20<span class="cite-bracket">]</span></a></sup>，歐拉也寫了連分數和佩爾方程的關係<sup id="cite_ref-FOOTNOTEWeil1984183_24-0" class="reference"><a href="#cite_note-FOOTNOTEWeil1984183-24"><span class="cite-bracket">[</span>21<span class="cite-bracket">]</span></a></sup>。</li> <li><i>二次式</i>，繼費馬之後，歐拉繼續研究哪些質數可以表示為<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x^{2}+Ny^{2}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>N</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+Ny^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/de0d4c34b673da9926f76d0642c4ba92e09e882d" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.503ex; height:3.009ex;" alt="{\displaystyle x^{2}+Ny^{2}}"></span>，其中有些顯示<a href="/wiki/%E4%BA%8C%E6%AC%A1%E4%BA%92%E5%8F%8D%E5%BE%8B" title="二次互反律">二次互反律</a>的性質<sup id="cite_ref-FOOTNOTEVaradarajan200644–47_25-0" class="reference"><a href="#cite_note-FOOTNOTEVaradarajan200644–47-25"><span class="cite-bracket">[</span>22<span class="cite-bracket">]</span></a></sup> <sup id="cite_ref-FOOTNOTEWeil1984177–179_26-0" class="reference"><a href="#cite_note-FOOTNOTEWeil1984177–179-26"><span class="cite-bracket">[</span>23<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEEdwards1983285–291_27-0" class="reference"><a href="#cite_note-FOOTNOTEEdwards1983285–291-27"><span class="cite-bracket">[</span>24<span class="cite-bracket">]</span></a></sup>。</li> <li><a href="/wiki/%E4%B8%9F%E7%95%AA%E5%9C%96%E6%96%B9%E7%A8%8B" title="丟番圖方程">丟番圖方程</a>：<a href="/wiki/%E6%AD%90%E6%8B%89" class="mw-redirect" title="歐拉">歐拉</a>研究一些<a href="/wiki/%E4%BA%8F%E6%A0%BC" title="亏格">虧格</a>為0或1的<a href="/wiki/%E4%B8%9F%E7%95%AA%E5%9C%96%E6%96%B9%E7%A8%8B" title="丟番圖方程">丟番圖方程</a><sup id="cite_ref-FOOTNOTEVaradarajan200655–56_28-0" class="reference"><a href="#cite_note-FOOTNOTEVaradarajan200655–56-28"><span class="cite-bracket">[</span>25<span class="cite-bracket">]</span></a></sup><sup id="cite_ref-FOOTNOTEWeil1984179–181_29-0" class="reference"><a href="#cite_note-FOOTNOTEWeil1984179–181-29"><span class="cite-bracket">[</span>26<span class="cite-bracket">]</span></a></sup>，特別的是他研讀丟番圖的著作，試圖要找到系統化的方法，但時機尚不成熟，幾何數論才剛形成而已<sup id="cite_ref-FOOTNOTEWeil1984181_30-0" class="reference"><a href="#cite_note-FOOTNOTEWeil1984181-30"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>。歐拉有注意到丟番圖方程和<a href="/wiki/%E6%A4%AD%E5%9C%86%E7%A7%AF%E5%88%86" title="椭圆积分">椭圆积分</a>之間的關係<sup id="cite_ref-FOOTNOTEWeil1984181_30-1" class="reference"><a href="#cite_note-FOOTNOTEWeil1984181-30"><span class="cite-bracket">[</span>27<span class="cite-bracket">]</span></a></sup>。</li></ul> <div class="mw-heading mw-heading2"><h2 id="分支"><span id=".E5.88.86.E6.94.AF"></span>分支</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=8" title="编辑章节：分支"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <dl><dt><a href="/wiki/%E5%88%9D%E7%AD%89%E6%95%B8%E8%AB%96" title="初等數論">初等數論</a></dt> <dd>意指使用不超過高中程度的初等代數處理的數論問題，最主要的工具包括整數的整除性與同餘。重要的結論包括<a href="/wiki/%E4%B8%AD%E5%9B%BD%E4%BD%99%E6%95%B0%E5%AE%9A%E7%90%86" class="mw-redirect" title="中国余数定理">中國餘數定理</a>、<a href="/wiki/%E8%B2%BB%E9%A6%AC%E5%B0%8F%E5%AE%9A%E7%90%86" class="mw-redirect" title="費馬小定理">費馬小定理</a>、<a href="/wiki/%E4%BA%8C%E6%AC%A1%E4%BA%92%E5%8F%8D%E5%BE%8B" title="二次互反律">二次互反律</a>等等。</dd></dl> <dl><dt><a href="/wiki/%E8%A7%A3%E6%9E%90%E6%95%B8%E8%AB%96" class="mw-redirect" title="解析數論">解析數論</a></dt> <dd>借助<a href="/wiki/%E5%BE%AE%E7%A9%8D%E5%88%86" class="mw-redirect" title="微積分">微積分</a>及<a href="/wiki/%E8%A4%87%E5%88%86%E6%9E%90" title="複分析">複分析</a>的技術來研究關於整數的問題<sup id="cite_ref-31" class="reference"><a href="#cite_note-31"><span class="cite-bracket">[</span>28<span class="cite-bracket">]</span></a></sup>，主要又可以分為<span class="ilh-all" data-orig-title="積性數論" data-lang-code="en" data-lang-name="英语" data-foreign-title="Multiplicative number theory"><span class="ilh-page"><a href="/w/index.php?title=%E7%A9%8D%E6%80%A7%E6%95%B8%E8%AB%96&action=edit&redlink=1" class="new" title="積性數論（页面不存在）">積性數論</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Multiplicative_number_theory" class="extiw" title="en:Multiplicative number theory"><span lang="en" dir="auto">Multiplicative number theory</span></a></span>）</span></span>與<a href="/wiki/%E5%8A%A0%E6%80%A7%E6%95%B8%E8%AB%96" class="mw-redirect" title="加性數論">加性數論</a>兩類。積性數論藉由研究積性生成函數的性質來探討質數分佈的問題，其中<a href="/wiki/%E8%B3%AA%E6%95%B8%E5%AE%9A%E7%90%86" title="質數定理">質數定理</a>與<a href="/wiki/%E7%8B%84%E5%88%A9%E5%85%8B%E9%9B%B7%E5%AE%9A%E7%90%86" title="狄利克雷定理">狄利克雷定理</a>為這個領域中最著名的古典成果。加性數論則是研究整數的加法分解之可能性與表示的問題，<a href="/wiki/%E8%8F%AF%E6%9E%97%E5%95%8F%E9%A1%8C" title="華林問題">華林問題</a>是該領域最著名的課題。此外例如<a href="/wiki/%E7%AD%9B%E6%B3%95" title="筛法">篩法</a>、<a href="/wiki/%E5%93%88%E4%BB%A3-%E6%9D%8E%E7%89%B9%E7%88%BE%E4%BC%8D%E5%BE%B7%E5%9C%93%E6%B3%95" title="哈代-李特爾伍德圓法">圓法</a>等等都是屬於這個範疇的重要議題。</dd> <dt><a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B8%E8%AB%96" title="代數數論">代數數論</a></dt> <dd>引申<a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B8" title="代數數">代數數</a>的話題，關於<a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B4%E6%95%B8" title="代數整數">代數整數</a>的研究，主要的研究目標是為了更一般地解決<a href="/wiki/%E4%B8%8D%E5%AE%9A%E6%96%B9%E7%A8%8B" class="mw-redirect" title="不定方程">不定方程</a>的問題，而為了達到此目的，這個領域與<a href="/wiki/%E4%BB%A3%E6%95%B8%E5%B9%BE%E4%BD%95" class="mw-redirect" title="代數幾何">代數幾何</a>之間有相當關聯，比如<a href="/wiki/%E9%A1%9E%E5%9F%9F%E8%AB%96" title="類域論">類域論</a>（class field theory）就是此間的顛峰之作。</dd> <dt><a href="/w/index.php?title=%E7%AE%97%E8%A1%93%E4%BB%A3%E6%95%B0%E5%B9%BE%E4%BD%95&action=edit&redlink=1" class="new" title="算術代数幾何（页面不存在）">算術代数幾何</a></dt> <dd>研究有理係數多變數方程組的有理點，其結構（主要是個數）和該方程組對應的代數簇的幾何性質之間的關係，有名的<a href="/wiki/%E8%B2%BB%E9%A6%AC%E6%9C%80%E5%BE%8C%E5%AE%9A%E7%90%86" class="mw-redirect" title="費馬最後定理">費馬最後定理</a>、莫德爾猜想（<a href="/wiki/%E6%B3%95%E7%88%BE%E5%BB%B7%E6%96%AF%E5%AE%9A%E7%90%86" class="mw-redirect" title="法爾廷斯定理">法爾廷斯定理</a>）、<span class="ilh-all" data-orig-title="Weil猜想" data-lang-code="en" data-lang-name="英语" data-foreign-title="Weil conjectures"><span class="ilh-page"><a href="/w/index.php?title=Weil%E7%8C%9C%E6%83%B3&action=edit&redlink=1" class="new" title="Weil猜想（页面不存在）">Weil猜想</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Weil_conjectures" class="extiw" title="en:Weil conjectures"><span lang="en" dir="auto">Weil conjectures</span></a></span>）</span></span>，和千禧年大獎難題中的<a href="/wiki/%E8%B2%9D%E8%B5%AB%E5%92%8C%E6%96%AF%E7%B6%AD%E8%A8%A5%E9%80%9A-%E6%88%B4%E7%88%BE%E7%8C%9C%E6%83%B3" class="mw-redirect" title="貝赫和斯維訥通-戴爾猜想">貝赫和斯維訥通-戴爾猜想</a>都屬此類。</dd> <dt><a href="/wiki/%E5%87%A0%E4%BD%95%E6%95%B0%E8%AE%BA" title="几何数论">幾何数论</a></dt> <dd>主要在於透過幾何觀點研究整數（在此即格子點）的分佈情形。最著名的定理為<a href="/wiki/%E9%97%B5%E5%8F%AF%E5%A4%AB%E6%96%AF%E5%9F%BA%E5%AE%9A%E7%90%86" class="mw-redirect" title="闵可夫斯基定理">闵可夫斯基定理</a>。</dd> <dt><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%95%B0%E8%AE%BA" title="计算数论">計算数论</a></dt> <dd>借助電腦的<a href="/wiki/%E7%AE%97%E6%B3%95" title="算法">算法</a>幫助數論的問題，例如素數測試和<a href="/wiki/%E5%9B%A0%E6%95%B0%E5%88%86%E8%A7%A3" class="mw-redirect" title="因数分解">因數分解</a>等和<a href="/wiki/%E5%AF%86%E7%A2%BC%E5%AD%B8" class="mw-redirect" title="密碼學">密碼學</a>息息相關的話題。</dd> <dt><a href="/wiki/%E8%B6%85%E8%B6%8A%E6%95%B8%E8%AB%96" title="超越數論">超越数论</a></dt> <dd>研究數的超越性，其中對於<a href="/wiki/%E6%AC%A7%E6%8B%89-%E9%A9%AC%E6%AD%87%E7%BD%97%E5%B0%BC%E5%B8%B8%E6%95%B0" class="mw-redirect" title="欧拉-马歇罗尼常数">歐拉常數</a>與特定的<a href="/wiki/%E9%BB%8E%E6%9B%BC%CE%B6%E5%87%BD%E6%95%B8" title="黎曼ζ函數">黎曼ζ函數</a>值之研究尤其令人感到興趣。</dd> <dt><a href="/wiki/%E7%BB%84%E5%90%88%E6%95%B0%E8%AE%BA" class="mw-redirect" title="组合数论">組合数论</a></dt> <dd>利用組合和機率的技巧，非構造性地證明某些無法用初等方式處理的複雜結論。這是由<a href="/wiki/%E4%BF%9D%E7%BD%97%C2%B7%E5%9F%83%E5%B0%94%E5%BE%B7%E4%BB%80" class="mw-redirect" title="保罗·埃尔德什">保罗·埃尔德什</a>開創的思路。</dd> <dt><a href="/wiki/%E6%A8%A1%E5%BD%A2%E5%BC%8F" title="模形式">模形式</a></dt> <dd>數學上一個滿足一些泛函方程與增長條件、在上半平面上的（複）<a href="/wiki/%E8%A7%A3%E6%9E%90%E5%87%BD%E6%95%B8" class="mw-redirect" title="解析函數">解析函數</a>。</dd></dl> <div class="mw-heading mw-heading2"><h2 id="應用"><span id=".E6.87.89.E7.94.A8"></span>應用</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=9" title="编辑章节：應用"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a href="/wiki/%E5%AF%86%E7%A2%BC%E5%AD%B8" class="mw-redirect" title="密碼學">密碼學</a></li> <li><a href="/wiki/%E5%AD%99%E5%AD%90%E5%AE%9A%E7%90%86" class="mw-redirect" title="孙子定理">孙子定理</a></li> <li><a href="/wiki/%E7%B4%A0%E6%95%B0" class="mw-redirect" title="素数">素数</a></li> <li><a href="/wiki/%E5%93%A5%E5%BE%B7%E5%B7%B4%E8%B5%AB%E7%8C%9C%E6%83%B3" title="哥德巴赫猜想">哥德巴赫猜想</a></li> <li><a href="/wiki/%E7%B4%A0%E6%95%B0%E5%85%AC%E5%BC%8F" title="素数公式">素数公式</a></li> <li><a href="/wiki/%E5%9F%83%E6%8B%89%E6%89%98%E6%96%AF%E7%89%B9%E5%B0%BC%E7%AD%9B%E6%B3%95" title="埃拉托斯特尼筛法">埃拉托斯特尼筛法</a></li> <li><a href="/wiki/%E5%8F%8C%E7%94%9F%E8%B4%A8%E6%95%B0" class="mw-redirect" title="双生质数">双生质数</a></li> <li><a href="/wiki/%E6%9C%89%E9%99%90%E5%9F%9F" title="有限域">有限域</a></li> <li><a href="/wiki/P%E9%80%B2%E6%95%B8" title="P進數">p進數</a></li></ul> <div class="mw-heading mw-heading2"><h2 id="注释"><span id=".E6.B3.A8.E9.87.8A"></span>注释</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=10" title="编辑章节：注释"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div id="references-NoteFoot"><ol class="references"> <li id="cite_note-2"><span class="mw-cite-backlink"><b><a href="#cite_ref-2">^</a></b></span> <span class="reference-text">德语原文“Die Mathematik ist die Königin der Wissenschaften, und die Arithmetik ist die Königin der Mathematik.”</span> </li> <li id="cite_note-4"><span class="mw-cite-backlink"><b><a href="#cite_ref-4">^</a></b></span> <span class="reference-text">1952年時數學家<span class="ilh-all" data-orig-title="哈罗德·达文波特" data-lang-code="en" data-lang-name="英语" data-foreign-title="Harold Davenport"><span class="ilh-page"><a href="/w/index.php?title=%E5%93%88%E7%BD%97%E5%BE%B7%C2%B7%E8%BE%BE%E6%96%87%E6%B3%A2%E7%89%B9&action=edit&redlink=1" class="new" title="哈罗德·达文波特（页面不存在）">哈罗德·达文波特</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Harold_Davenport" class="extiw" title="en:Harold Davenport"><span lang="en" dir="auto">Harold Davenport</span></a></span>）</span></span>仍用「高等算術」一詞來表示數論，<a href="/wiki/%E6%88%88%E5%BC%97%E9%9B%B7%C2%B7%E5%93%88%E7%BD%97%E5%BE%B7%C2%B7%E5%93%88%E4%BB%A3" title="戈弗雷·哈罗德·哈代">戈弗雷·哈羅德·哈代</a>和<a href="/wiki/%E6%84%9B%E5%BE%B7%E8%8F%AF%C2%B7%E6%A2%85%E7%89%B9%E8%98%AD%C2%B7%E8%B3%B4%E7%89%B9" title="愛德華·梅特蘭·賴特">愛德華·梅特蘭·賴特</a>在1938年寫《數論介紹》簡介時曾提到「我們曾考慮過將書名改為《算術介紹》，某方面而言是更合適的書名，但也容易讓讀者誤會其中的內容」<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></span> </li> <li id="cite_note-5"><span class="mw-cite-backlink"><b><a href="#cite_ref-5">^</a></b></span> <span class="reference-text">不過在20世紀的後半，有部份數學家仍會用「算術」一詞來表示數論。到20世紀初，才開始使用數論的名稱</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="參考資料"><span id=".E5.8F.83.E8.80.83.E8.B3.87.E6.96.99"></span>參考資料</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=11" title="编辑章节：參考資料"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="reflist columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em; list-style-type: decimal;"> <ol class="references"> <li id="cite_note-1"><span class="mw-cite-backlink"><b><a href="#cite_ref-1">^</a></b></span> <span class="reference-text"><cite class="citation web"><a rel="nofollow" class="external text" href="http://www.gresham.ac.uk/lectures-and-events/the-queen-of-mathematics">The Queen of Mathematics</a>. <span class="reference-accessdate"> [<span class="nowrap">2014-09-30</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20141006100109/http://www.gresham.ac.uk/lectures-and-events/the-queen-of-mathematics">存档</a>于2014-10-06）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.btitle=The+Queen+of+Mathematics&rft.genre=unknown&rft_id=http%3A%2F%2Fwww.gresham.ac.uk%2Flectures-and-events%2Fthe-queen-of-mathematics&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-3"><span class="mw-cite-backlink"><b><a href="#cite_ref-3">^</a></b></span> <span class="reference-text"><cite class="citation journal">Apostol, Tom M. <a rel="nofollow" class="external text" href="http://www.ams.org/mathscinet/">An introduction to the theory of numbers</a>. (Review of Hardy & Wright.) Mathematical Reviews (MathSciNet) MR0568909. American Mathematical Society. n.d. <span class="reference-accessdate"> [<span class="nowrap">2013-05-06</span>]</span>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20120731035922/http://www.ams.org/mathscinet/">存档</a>于2012-07-31）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.atitle=An+introduction+to+the+theory+of+numbers&rft.aufirst=Tom+M.&rft.aulast=Apostol&rft.chron=n.d.&rft.genre=article&rft_id=http%3A%2F%2Fwww.ams.org%2Fmathscinet%2F&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span></span> </li> <li id="cite_note-6"><span class="mw-cite-backlink"><b><a href="#cite_ref-6">^</a></b></span> <span class="reference-text"><cite id="CITEREFHeath1921" class="citation book"><a href="/w/index.php?title=Thomas_Little_Heath&action=edit&redlink=1" class="new" title="Thomas Little Heath（页面不存在）">Heath, Thomas L.</a> <a rel="nofollow" class="external text" href="https://archive.org/details/historyofgreekma01heat">A History of Greek Mathematics, Volume 1: From Thales to Euclid</a>. Oxford: Clarendon Press. 1921 <span class="reference-accessdate"> [<span class="nowrap">2016-02-28</span>]</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.aufirst=Thomas+L.&rft.aulast=Heath&rft.btitle=A+History+of+Greek+Mathematics%2C+Volume+1%3A+From+Thales+to+Euclid&rft.date=1921&rft.genre=book&rft.place=Oxford&rft.pub=Clarendon+Press&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fhistoryofgreekma01heat&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> </span> </li> <li id="cite_note-FOOTNOTEWeil198445–46-7"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil198445–46_7-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第45–46頁.</span> </li> <li id="cite_note-8"><span class="mw-cite-backlink"><b><a href="#cite_ref-8">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第118頁，數論比其他數學領域容易出現這様的情形（說明在<a href="#CITEREFMahoney1994">Mahoney 1994</a>，第284頁）</span> </li> <li id="cite_note-9"><span class="mw-cite-backlink"><b><a href="#cite_ref-9">^</a></b></span> <span class="reference-text"><a href="#CITEREFMahoney1994">Mahoney 1994</a>，第48, 53–54頁</span> </li> <li id="cite_note-FOOTNOTEWeil198453-10"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil198453_10-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第53頁.</span> </li> <li id="cite_note-11"><span class="mw-cite-backlink"><b><a href="#cite_ref-11">^</a></b></span> <span class="reference-text"><a href="#CITEREFTanneryHenry1891">Tannery & Henry 1891</a>，Vol. II, p. 209, Letter XLVI from Fermat to Frenicle, 1640, cited in <a href="#CITEREFWeil1984">Weil 1984</a>，第56頁</span> </li> <li id="cite_note-12"><span class="mw-cite-backlink"><b><a href="#cite_ref-12">^</a></b></span> <span class="reference-text"><a href="#CITEREFTanneryHenry1891">Tannery & Henry 1891</a>，Vol. II, p. 204, cited in <a href="#CITEREFWeil1984">Weil 1984</a>，第63頁</span> </li> <li id="cite_note-FOOTNOTETanneryHenry1891Vol._II,_p._213-13"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTETanneryHenry1891Vol._II,_p._213_13-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTanneryHenry1891">Tannery & Henry 1891</a>，Vol. II, p. 213.</span> </li> <li id="cite_note-FOOTNOTETanneryHenry1891Vol._II,_p._423-14"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTETanneryHenry1891Vol._II,_p._423_14-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFTanneryHenry1891">Tannery & Henry 1891</a>，Vol. II, p. 423.</span> </li> <li id="cite_note-FOOTNOTEWeil198480,_91–92-15"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil198480,_91–92_15-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第80, 91–92頁.</span> </li> <li id="cite_note-FOOTNOTEWeil198492-16"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil198492_16-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第92頁.</span> </li> <li id="cite_note-FOOTNOTEWeil1984Ch._II,_sect._XV_and_XVI-17"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil1984Ch._II,_sect._XV_and_XVI_17-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，Ch. II, sect. XV and XVI.</span> </li> <li id="cite_note-FOOTNOTEWeil1984104-18"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil1984104_18-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第104頁.</span> </li> <li id="cite_note-FOOTNOTEWeil19842,_172-19"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil19842,_172_19-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第2, 172頁.</span> </li> <li id="cite_note-FOOTNOTEVaradarajan20069-20"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVaradarajan20069_20-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVaradarajan2006">Varadarajan 2006</a>，第9頁.</span> </li> <li id="cite_note-21"><span class="mw-cite-backlink"><b><a href="#cite_ref-21">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第2頁 and <a href="#CITEREFVaradarajan2006">Varadarajan 2006</a>，第37頁</span> </li> <li id="cite_note-22"><span class="mw-cite-backlink"><b><a href="#cite_ref-22">^</a></b></span> <span class="reference-text"><a href="#CITEREFVaradarajan2006">Varadarajan 2006</a>，第39頁 and <a href="#CITEREFWeil1984">Weil 1984</a>，第176–189頁</span> </li> <li id="cite_note-Eulpell-23"><span class="mw-cite-backlink"><b><a href="#cite_ref-Eulpell_23-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第174頁</span> </li> <li id="cite_note-FOOTNOTEWeil1984183-24"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil1984183_24-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第183頁.</span> </li> <li id="cite_note-FOOTNOTEVaradarajan200644–47-25"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVaradarajan200644–47_25-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVaradarajan2006">Varadarajan 2006</a>，第44–47頁.</span> </li> <li id="cite_note-FOOTNOTEWeil1984177–179-26"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil1984177–179_26-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第177–179頁.</span> </li> <li id="cite_note-FOOTNOTEEdwards1983285–291-27"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEEdwards1983285–291_27-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFEdwards1983">Edwards 1983</a>，第285–291頁.</span> </li> <li id="cite_note-FOOTNOTEVaradarajan200655–56-28"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEVaradarajan200655–56_28-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFVaradarajan2006">Varadarajan 2006</a>，第55–56頁.</span> </li> <li id="cite_note-FOOTNOTEWeil1984179–181-29"><span class="mw-cite-backlink"><b><a href="#cite_ref-FOOTNOTEWeil1984179–181_29-0">^</a></b></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第179–181頁.</span> </li> <li id="cite_note-FOOTNOTEWeil1984181-30"><span class="mw-cite-backlink">^ <a href="#cite_ref-FOOTNOTEWeil1984181_30-0"><sup><b>27.0</b></sup></a> <a href="#cite_ref-FOOTNOTEWeil1984181_30-1"><sup><b>27.1</b></sup></a></span> <span class="reference-text"><a href="#CITEREFWeil1984">Weil 1984</a>，第181頁.</span> </li> <li id="cite_note-31"><span class="mw-cite-backlink"><b><a href="#cite_ref-31">^</a></b></span> <span class="reference-text"><cite id="CITEREFApostol1976" class="citation"><a href="/wiki/Tom_M._Apostol" class="mw-redirect" title="Tom M. Apostol">Apostol, Tom M.</a>, Introduction to analytic number theory, Undergraduate Texts in Mathematics, New York-Heidelberg: <a href="/wiki/Springer-Verlag" class="mw-redirect" title="Springer-Verlag">Springer-Verlag</a>, 1976, <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-387-90163-3" title="Special:网络书源/978-0-387-90163-3"><span title="国际标准书号">ISBN</span> 978-0-387-90163-3</a>, <a rel="nofollow" class="external text" href="//www.ams.org/mathscinet-getitem?mr=0434929"><span title="數學評論">MR 0434929</span></a>, <a rel="nofollow" class="external text" href="//zbmath.org/?format=complete&q=an:0335.10001"><span title="Zentralblatt MATH">Zbl 0335.10001</span></a></cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.aufirst=Tom+M.&rft.aulast=Apostol&rft.btitle=Introduction+to+analytic+number+theory&rft.date=1976&rft.genre=book&rft.isbn=978-0-387-90163-3&rft.place=New+York-Heidelberg&rft.pub=Springer-Verlag&rft.series=Undergraduate+Texts+in+Mathematics&rft_id=%2F%2Fwww.ams.org%2Fmathscinet-getitem%3Fmr%3D0434929&rft_id=%2F%2Fzbmath.org%2F%3Fformat%3Dcomplete%26q%3Dan%3A0335.10001&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="參考書目"><span id=".E5.8F.83.E8.80.83.E6.9B.B8.E7.9B.AE"></span>參考書目</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=12" title="编辑章节：參考書目"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <style data-mw-deduplicate="TemplateStyles:r80540462">.mw-parser-output .refbegin{font-size:90%;margin-bottom:0.5em}.mw-parser-output .refbegin-hanging-indents>ul{margin-left:0}.mw-parser-output .refbegin-hanging-indents>ul>li{margin-left:0;padding-left:3.2em;text-indent:-3.2em}.mw-parser-output .refbegin-hanging-indents ul,.mw-parser-output .refbegin-hanging-indents ul li{list-style:none}@media(max-width:720px){.mw-parser-output .refbegin-hanging-indents>ul>li{padding-left:1.6em;text-indent:-1.6em}}.mw-parser-output .refbegin-columns{margin-top:0.3em}.mw-parser-output .refbegin-columns ul{margin-top:0}.mw-parser-output .refbegin-columns li{page-break-inside:avoid;break-inside:avoid-column}.mw-parser-output .refbegin-100{font-size:100%}</style><div class="refbegin columns references-column-width" style="-moz-column-width: 30em; -webkit-column-width: 30em; column-width: 30em;"> <ul><li><cite id="CITEREFWeil1984" class="citation book"><a href="/wiki/%E5%AE%89%E5%BE%B7%E7%83%88%C2%B7%E9%9F%A6%E4%BC%8A" title="安德烈·韦伊">Weil, André</a>. <a rel="nofollow" class="external text" href="http://books.google.co.uk/books?id=XSV0hDFj3loC">Number theory: an approach through history – from Hammurapi to Legendre,</a>. Boston: Birkhäuser. 1984 <span class="reference-accessdate"> [<span class="nowrap">2014-10-06</span>]</span>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-8176-3141-3" title="Special:网络书源/978-0-8176-3141-3"><span title="国际标准书号">ISBN</span> 978-0-8176-3141-3</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20141012145013/http://books.google.co.uk/books?id=XSV0hDFj3loC">存档</a>于2014-10-12）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.aufirst=Andr%C3%A9&rft.aulast=Weil&rft.btitle=Number+theory%3A+an+approach+through+history+%E2%80%93+from+Hammurapi+to+Legendre%2C&rft.date=1984&rft.genre=book&rft.isbn=978-0-8176-3141-3&rft.place=Boston&rft.pub=Birkh%C3%A4user&rft_id=http%3A%2F%2Fbooks.google.co.uk%2Fbooks%3Fid%3DXSV0hDFj3loC&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFMahoney1994" class="citation book">Mahoney, M. S. <a rel="nofollow" class="external text" href="http://books.google.co.uk/books?id=My19IcewAnoC">The mathematical career of Pierre de Fermat, 1601–1665</a> Reprint, 2nd. Princeton University Press. 1994 <span class="reference-accessdate"> [<span class="nowrap">2014-10-06</span>]</span>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-691-03666-3" title="Special:网络书源/978-0-691-03666-3"><span title="国际标准书号">ISBN</span> 978-0-691-03666-3</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20141012144521/http://books.google.co.uk/books?id=My19IcewAnoC">存档</a>于2014-10-12）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.aufirst=M.+S.&rft.aulast=Mahoney&rft.btitle=The+mathematical+career+of+Pierre+de+Fermat%2C+1601%E2%80%931665&rft.date=1994&rft.edition=Reprint%2C+2nd&rft.genre=book&rft.isbn=978-0-691-03666-3&rft.pub=Princeton+University+Press&rft_id=http%3A%2F%2Fbooks.google.co.uk%2Fbooks%3Fid%3DMy19IcewAnoC&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFTanneryHenry1891" class="citation book">Tannery, Paul; Henry, Charles (eds.); <a href="/wiki/%E7%9A%AE%E5%9F%83%E7%88%BE%C2%B7%E5%BE%B7%C2%B7%E8%B2%BB%E9%A6%AC" title="皮埃爾·德·費馬">Fermat, Pierre de</a>. Oeuvres de Fermat. (4 Vols.). Paris: Imprimerie Gauthier-Villars et Fils. 1891 <span style="font-family: sans-serif; cursor: default; color:var(--color-subtle, #54595d); font-size: 0.8em; bottom: 0.1em; font-weight: bold;" title="连接到法语及拉丁语网页">（法语及拉丁语）</span>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.au=Fermat%2C+Pierre+de&rft.au=Henry%2C+Charles+%28eds.%29&rft.aufirst=Paul&rft.aulast=Tannery&rft.btitle=Oeuvres+de+Fermat&rft.date=1891&rft.genre=book&rft.place=Paris&rft.pub=Imprimerie+Gauthier-Villars+et+Fils&rft.series=%284+Vols.%29&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span> <a rel="nofollow" class="external text" href="https://archive.org/details/oeuvresdefermat01ferm">Volume 1</a> <a rel="nofollow" class="external text" href="https://archive.org/details/oeuvresdefermat02ferm">Volume 2</a> <a rel="nofollow" class="external text" href="https://archive.org/details/oeuvresdefermat03ferm">Volume 3</a> <a rel="nofollow" class="external text" href="https://archive.org/details/oeuvresdefermat04ferm">Volume 4 (1912)</a></li> <li><cite id="CITEREFVaradarajan2006" class="citation book">Varadarajan, V. S. <a rel="nofollow" class="external text" href="http://books.google.co.uk/books?id=CYyKTREGYd0C">Euler through time: a new look at old themes</a>. American Mathematical Society. 2006 <span class="reference-accessdate"> [<span class="nowrap">2014-10-06</span>]</span>. <a href="/wiki/Special:%E7%BD%91%E7%BB%9C%E4%B9%A6%E6%BA%90/978-0-8218-3580-7" title="Special:网络书源/978-0-8218-3580-7"><span title="国际标准书号">ISBN</span> 978-0-8218-3580-7</a>. （原始内容<a rel="nofollow" class="external text" href="https://web.archive.org/web/20141012194254/http://books.google.co.uk/books?id=CYyKTREGYd0C">存档</a>于2014-10-12）.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.aufirst=V.+S.&rft.aulast=Varadarajan&rft.btitle=Euler+through+time%3A+a+new+look+at+old+themes&rft.date=2006&rft.genre=book&rft.isbn=978-0-8218-3580-7&rft.pub=American+Mathematical+Society&rft_id=http%3A%2F%2Fbooks.google.co.uk%2Fbooks%3Fid%3DCYyKTREGYd0C&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Abook" class="Z3988"><span style="display:none;"> </span></span></li> <li><cite id="CITEREFEdwards1983" class="citation journal">Edwards, Harold M. <a rel="nofollow" class="external text" href="https://archive.org/details/sim_mathematics-magazine_1983-11_56_5/page/285">Euler and quadratic reciprocity</a>. Mathematics Magazine (Mathematical Association of America). November 1983, <b>56</b> (5): 285–291. <a rel="nofollow" class="external text" href="//www.jstor.org/stable/2690368"><span title="JSTOR">JSTOR 2690368</span></a>. <a rel="nofollow" class="external text" href="https://doi.org/10.2307%2F2690368"><span title="數位物件識別號">doi:10.2307/2690368</span></a>.</cite><span title="ctx_ver=Z39.88-2004&rfr_id=info%3Asid%2Fzh.wikipedia.org%3A%E6%95%B0%E8%AE%BA&rft.atitle=Euler+and+quadratic+reciprocity&rft.aufirst=Harold+M.&rft.aulast=Edwards&rft.date=1983-11&rft.genre=article&rft.issue=5&rft.jtitle=Mathematics+Magazine&rft.pages=285-291&rft.volume=56&rft_id=%2F%2Fwww.jstor.org%2Fstable%2F2690368&rft_id=https%3A%2F%2Farchive.org%2Fdetails%2Fsim_mathematics-magazine_1983-11_56_5%2Fpage%2F285&rft_id=info%3Adoi%2F10.2307%2F2690368&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal" class="Z3988"><span style="display:none;"> </span></span><span class="citation-comment" style="display:none; color:#33aa33"> 引文格式1维护：日期与年 (<a href="/wiki/Category:%E5%BC%95%E6%96%87%E6%A0%BC%E5%BC%8F1%E7%BB%B4%E6%8A%A4%EF%BC%9A%E6%97%A5%E6%9C%9F%E4%B8%8E%E5%B9%B4" title="Category:引文格式1维护：日期与年">link</a>)</span></li></ul> </div> <div class="mw-heading mw-heading2"><h2 id="外部連結"><span id=".E5.A4.96.E9.83.A8.E9.80.A3.E7.B5.90"></span>外部連結</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E6%95%B0%E8%AE%BA&action=edit&section=13" title="编辑章节：外部連結"><span>编辑</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><span style="font-family: sans-serif; cursor: default; color:var(--color-subtle, #54595d); font-size: 0.8em; bottom: 0.1em; font-weight: bold;" title="英語">（英文）</span> <a rel="nofollow" class="external text" href="http://www.numbertheory.org/">Number Theory Web</a> （<a rel="nofollow" class="external text" href="//web.archive.org/web/20190618181516/http://www.numbertheory.org/">页面存档备份</a>，存于<a href="/wiki/%E4%BA%92%E8%81%94%E7%BD%91%E6%A1%A3%E6%A1%88%E9%A6%86" title="互联网档案馆">互联网档案馆</a>）</li></ul> <div style="clear: both; height: 1em"></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><style data-mw-deduplicate="TemplateStyles:r84261037">.mw-parser-output .navbox{box-sizing:border-box;border:1px solid #a2a9b1;width:100%;clear:both;font-size:88%;text-align:center;padding:1px;margin:1em auto 0}.mw-parser-output .navbox .navbox{margin-top:0}.mw-parser-output .navbox+.navbox,.mw-parser-output .navbox+.navbox-styles+.navbox{margin-top:-1px}.mw-parser-output .navbox-inner,.mw-parser-output .navbox-subgroup{width:100%}.mw-parser-output .navbox-group,.mw-parser-output .navbox-title,.mw-parser-output .navbox-abovebelow{text-align:center;padding-left:1em;padding-right:1em}.mw-parser-output .navbox-group{white-space:nowrap;text-align:right}.mw-parser-output .navbox,.mw-parser-output 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dl,.mw-parser-output .navbox td.hlist ol,.mw-parser-output .navbox td.hlist ul{padding:0.125em 0}.mw-parser-output .navbox .navbar{display:block;font-size:100%}.mw-parser-output .navbox-title .navbar{float:left;text-align:left;margin-right:0.5em;width:auto;padding-left:0.2em;position:absolute;left:1em}.mw-parser-output .navbox .mw-collapsible-toggle{margin-left:0.5em;position:absolute;right:1em}body.skin--responsive .mw-parser-output .navbox-image img{max-width:none!important}@media print{body.ns-0 .mw-parser-output .navbox{display:none!important}}</style></div><div role="navigation" class="navbox" aria-labelledby="主要的数学领域" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="3"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E6%95%B0%E5%AD%A6%E9%A2%86%E5%9F%9F" title="Template:数学领域"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E6%95%B0%E5%AD%A6%E9%A2%86%E5%9F%9F" title="Template talk:数学领域"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E6%95%B0%E5%AD%A6%E9%A2%86%E5%9F%9F" title="Special:编辑页面/Template:数学领域"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="主要的数学领域" style="font-size:110%;margin:0 5em">主要的<a href="/wiki/%E6%95%B0%E5%AD%A6" title="数学">数学</a><a href="/wiki/%E6%95%B0%E5%AD%A6%E9%A2%86%E5%9F%9F" title="数学领域">领域</a></div></th></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%8F%B2" title="数学史">历史</a></li> <li><span class="ilh-all" data-orig-title="数学纲要" data-lang-code="en" data-lang-name="英语" data-foreign-title="Outline of mathematics"><span class="ilh-page"><a href="/w/index.php?title=%E6%95%B0%E5%AD%A6%E7%BA%B2%E8%A6%81&action=edit&redlink=1" class="new" title="数学纲要（页面不存在）">纲要</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Outline_of_mathematics" class="extiw" title="en:Outline of mathematics"><span lang="en" dir="auto">Outline of mathematics</span></a></span>）</span></span></li> <li><span class="ilh-all" data-orig-title="数学主题列表" data-lang-code="en" data-lang-name="英语" data-foreign-title="Lists of mathematics topics"><span class="ilh-page"><a href="/w/index.php?title=%E6%95%B0%E5%AD%A6%E4%B8%BB%E9%A2%98%E5%88%97%E8%A1%A8&action=edit&redlink=1" class="new" title="数学主题列表（页面不存在）">列表</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Lists_of_mathematics_topics" class="extiw" title="en:Lists of mathematics topics"><span lang="en" dir="auto">Lists of mathematics topics</span></a></span>）</span></span></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E7%AC%A6%E5%8F%B7%E8%A1%A8" title="数学符号表">符号表</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%9F%BA%E7%A1%80" title="数学基础">数学基础</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%8C%83%E7%95%B4%E8%AE%BA" title="范畴论">范畴论</a></li> <li><a href="/wiki/%E9%9B%86%E5%90%88%E8%AE%BA" title="集合论">集合论</a></li> <li><a href="/wiki/%E6%95%B0%E7%90%86%E9%80%BB%E8%BE%91" title="数理逻辑">数理逻辑</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%93%B2%E5%AD%A6" title="数学哲学">数学哲学</a></li></ul> </div></td><td class="noviewer navbox-image" rowspan="12" style="width:1px;padding:0px 0px 0px 2px"><div><span typeof="mw:File"><a href="/wiki/File:Math.svg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Math.svg/80px-Math.svg.png" decoding="async" width="80" height="80" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Math.svg/120px-Math.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/eb/Math.svg/160px-Math.svg.png 2x" data-file-width="800" data-file-height="800" /></a></span></div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E4%BB%A3%E6%95%B0" title="代数">代数</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%8A%BD%E8%B1%A1%E4%BB%A3%E6%95%B0" title="抽象代数">抽象</a></li> <li><a href="/wiki/%E4%BA%A4%E6%8F%9B%E4%BB%A3%E6%95%B8" title="交換代數">交換</a></li> <li><a href="/wiki/%E7%BE%A4%E8%AE%BA" title="群论">群论</a></li> <li><a href="/wiki/%E5%88%9D%E7%AD%89%E4%BB%A3%E6%95%B8" title="初等代數">初等代數</a></li> <li><a href="/wiki/%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0" title="线性代数">线性代数</a></li> <li><a href="/wiki/%E5%A4%9A%E9%87%8D%E7%BA%BF%E6%80%A7%E4%BB%A3%E6%95%B0" title="多重线性代数">多重线性代数</a></li> <li><a href="/wiki/%E6%B3%9B%E4%BB%A3%E6%95%B0" title="泛代数">泛代数</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%88%86%E6%9E%90" title="数学分析">数学分析</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%BE%AE%E7%A7%AF%E5%88%86" class="mw-redirect" title="微积分">微积分</a></li> <li><a href="/wiki/%E5%AE%9E%E5%8F%98%E5%87%BD%E6%95%B0%E8%AE%BA" title="实变函数论">实变函数</a></li> <li><a href="/wiki/%E8%A4%87%E5%88%86%E6%9E%90" title="複分析">复变函数</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E6%96%B9%E7%A8%8B" title="微分方程">微分方程</a></li> <li><a href="/wiki/%E6%B3%9B%E5%87%BD%E5%88%86%E6%9E%90" title="泛函分析">泛函分析</a></li> <li><a href="/wiki/%E8%AA%BF%E5%92%8C%E5%88%86%E6%9E%90" title="調和分析">調和分析</a></li> <li><a href="/wiki/%E5%82%85%E7%AB%8B%E5%8F%B6%E5%88%86%E6%9E%90" class="mw-redirect" title="傅立叶分析">傅立葉分析</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95%E5%88%86%E6%9E%90" title="几何分析">几何分析</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%A6%BB%E6%95%A3%E6%95%B0%E5%AD%A6" title="离散数学">离散数学</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%BB%84%E5%90%88%E6%95%B0%E5%AD%A6" title="组合数学">组合数学</a></li> <li><a href="/wiki/%E5%9B%BE%E8%AE%BA" title="图论">图论</a></li> <li><a href="/wiki/%E5%BA%8F%E7%90%86%E8%AE%BA" title="序理论">序理论</a></li> <li><a href="/wiki/%E5%8D%9A%E5%BC%88%E8%AE%BA" title="博弈论">博弈论</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%87%A0%E4%BD%95%E5%AD%A6" title="几何学">几何学</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E4%BB%A3%E6%95%B0%E5%87%A0%E4%BD%95" title="代数几何">代数几何</a></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E5%87%A0%E4%BD%95" title="解析几何">解析几何</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E5%87%A0%E4%BD%95" title="微分几何">微分几何</a></li> <li><a href="/wiki/%E7%A6%BB%E6%95%A3%E5%87%A0%E4%BD%95%E5%AD%A6" title="离散几何学">离散几何学</a></li> <li><a href="/wiki/%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="欧几里得几何">欧几里得几何</a></li> <li><a href="/wiki/%E9%9D%9E%E6%AC%A7%E5%87%A0%E9%87%8C%E5%BE%97%E5%87%A0%E4%BD%95" title="非欧几里得几何">非欧几里得几何</a></li> <li><a href="/wiki/%E6%9C%89%E9%99%90%E5%B9%BE%E4%BD%95%E5%AD%B8" title="有限幾何學">有限几何学</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a class="mw-selflink selflink">数论</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%AE%97%E6%9C%AF" title="算术">算术</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B8%E6%95%B8%E8%AB%96" title="代數數論">代數數論</a></li> <li><a href="/wiki/%E8%A7%A3%E6%9E%90%E6%95%B0%E8%AE%BA" title="解析数论">解析数论</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95%E6%95%B0%E8%AE%BA" title="几何数论">几何数论</a></li> <li><a href="/wiki/%E7%AE%97%E6%9C%AF%E5%87%A0%E4%BD%95" title="算术几何">算术几何</a></li> <li><a href="/wiki/%E4%B8%A2%E7%95%AA%E5%9B%BE%E5%87%A0%E4%BD%95" class="mw-redirect" title="丢番图几何">丢番图几何</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%8B%93%E6%89%91%E5%AD%A6" title="拓扑学">拓扑学</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%82%B9%E9%9B%86%E6%8B%93%E6%89%91%E5%AD%A6" title="点集拓扑学">点集拓扑</a></li> <li><a href="/wiki/%E4%BB%A3%E6%95%B0%E6%8B%93%E6%89%91" title="代数拓扑">代数拓扑</a></li> <li><a href="/wiki/%E5%BE%AE%E5%88%86%E6%8B%93%E6%89%91" title="微分拓扑">微分拓扑</a></li> <li><a href="/wiki/%E5%87%A0%E4%BD%95%E6%8B%93%E6%89%91%E5%AD%A6" title="几何拓扑学">几何拓扑</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6" title="统计学">统计学</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%B5%8B%E5%BA%A6" title="测度">测度与概率</a></li> <li><a href="/wiki/%E6%95%B0%E7%90%86%E7%BB%9F%E8%AE%A1%E5%AD%A6" title="数理统计学">数理统计学</a></li> <li><a href="/wiki/%E6%95%B0%E6%8D%AE%E7%A7%91%E5%AD%A6" title="数据科学">数据科学</a></li> <li><a href="/wiki/%E6%8E%A8%E8%AB%96%E7%B5%B1%E8%A8%88%E5%AD%B8" title="推論統計學">统计推断</a></li> <li><a href="/wiki/%E8%BF%B4%E6%AD%B8%E5%88%86%E6%9E%90" title="迴歸分析">迴歸分析</a></li> <li><a href="/wiki/%E7%BB%9F%E8%AE%A1%E5%AD%A6%E4%B9%A0%E7%90%86%E8%AE%BA" title="统计学习理论">统计学习理论</a></li> <li><a href="/wiki/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="机器学习">机器学习</a></li> <li><a href="/wiki/%E4%BA%BA%E5%B7%A5%E6%99%BA%E8%83%BD" title="人工智能">人工智能</a></li> <li><a href="/wiki/%E6%95%B0%E6%8D%AE%E7%BB%93%E6%9E%84" title="数据结构">数据结构</a>与<a href="/wiki/%E7%AE%97%E6%B3%95" title="算法">算法</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%BF%90%E7%AE%97%E6%95%B0%E5%AD%A6" title="运算数学">计算数学</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%A7%91%E5%AD%A6" title="计算机科学">计算机科学</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E7%90%86%E8%AE%BA" title="计算理论">计算理论</a></li> <li><a href="/wiki/%E6%95%B0%E5%80%BC%E5%88%86%E6%9E%90" title="数值分析">数值分析</a></li> <li><a href="/wiki/%E6%9C%80%E4%BC%98%E5%8C%96" title="最优化">最优化</a></li> <li><a href="/wiki/%E8%A8%88%E7%AE%97%E6%A9%9F%E4%BB%A3%E6%95%B8%E7%B3%BB%E7%B5%B1" title="計算機代數系統">计算机代数</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E5%BA%94%E7%94%A8%E6%95%B0%E5%AD%A6" title="应用数学">应用数学</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%8E%A7%E5%88%B6%E8%AE%BA" title="控制论">控制论</a></li> <li><a href="/wiki/%E4%BF%A1%E6%81%AF%E8%AE%BA" title="信息论">信息论</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E5%8C%96%E5%AD%A6" title="计算化学">计算化学</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E7%94%9F%E7%89%A9%E5%AD%B8" title="數理生物學">数理生物学</a></li> <li><a href="/wiki/%E6%95%B0%E7%90%86%E7%BB%8F%E6%B5%8E%E5%AD%A6" title="数理经济学">数理经济学</a></li> <li><a href="/wiki/%E8%AE%A1%E9%87%8F%E7%BB%8F%E6%B5%8E%E5%AD%A6" title="计量经济学">计量经济学</a></li> <li><a href="/wiki/%E6%95%B8%E7%90%86%E9%87%91%E8%9E%8D%E5%AD%B8" title="數理金融學">數理金融學</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E5%BF%83%E7%90%86%E5%AD%A6" title="数学心理学">数学心理学</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E7%89%A9%E7%90%86" title="数学物理">数学物理学</a></li> <li><a href="/wiki/%E7%94%9F%E7%89%A9%E7%B5%B1%E8%A8%88%E5%AD%B8" title="生物統計學">生物統計學</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">其它</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%A8%9B%E6%A8%82%E6%95%B8%E5%AD%B8" title="娛樂數學">娱乐数学</a></li> <li><span class="ilh-all" data-orig-title="数学与艺术" data-lang-code="en" data-lang-name="英语" data-foreign-title="Mathematics and art"><span class="ilh-page"><a href="/w/index.php?title=%E6%95%B0%E5%AD%A6%E4%B8%8E%E8%89%BA%E6%9C%AF&action=edit&redlink=1" class="new" title="数学与艺术（页面不存在）">数学与艺术</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Mathematics_and_art" class="extiw" title="en:Mathematics and art"><span lang="en" dir="auto">Mathematics and art</span></a></span>）</span></span></li> <li><a href="/wiki/%E6%95%B0%E5%AD%A6%E6%95%99%E8%82%B2" title="数学教育">数学教育</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">注释</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li>数学的领域也可根据“<a href="/wiki/%E6%95%B0%E5%AD%A6%E5%AD%A6%E7%A7%91%E5%88%86%E7%B1%BB%E6%A0%87%E5%87%86" title="数学学科分类标准">MSC分类标准</a>”或“<a href="/w/index.php?title=%E4%B8%AD%E5%9B%BD%E5%AD%A6%E7%A7%91%E5%88%86%E7%B1%BB%E5%9B%BD%E5%AE%B6%E6%A0%87%E5%87%86/110&action=edit&redlink=1" class="new" title="中国学科分类国家标准/110（页面不存在）">中国学科分类国家标准</a>”进行分类。</li></ul> </div></td></tr><tr><td class="navbox-abovebelow" colspan="3"><div> <ul><li><span typeof="mw:File"><span title="分类"><img alt="分类" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/16px-Symbol_category_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/23px-Symbol_category_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/96/Symbol_category_class.svg/31px-Symbol_category_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Category:%E6%95%B0%E5%AD%A6" title="Category:数学">分类</a></b></li> <li><span typeof="mw:File"><span title="主题"><img alt="主题" src="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/16px-Symbol_portal_class.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/23px-Symbol_portal_class.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/e/e2/Symbol_portal_class.svg/31px-Symbol_portal_class.svg.png 2x" data-file-width="180" data-file-height="185" /></span></span> <b><a href="/wiki/Portal:%E6%95%B0%E5%AD%A6" title="Portal:数学">主题</a></b></li> <li><span typeof="mw:File"><span title="共享资源页面"><img alt="共享资源页面" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/12px-Commons-logo.svg.png" decoding="async" width="12" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/18px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/24px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></span></span><b><a href="https://commons.wikimedia.org/wiki/Category:Mathematics" class="extiw" title="commons:Category:Mathematics">共享资源</a></b></li> <li><span typeof="mw:File"><span title="专题"><img alt="专题" src="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/16px-People_icon.svg.png" decoding="async" width="16" height="16" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/24px-People_icon.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/3/37/People_icon.svg/32px-People_icon.svg.png 2x" data-file-width="100" data-file-height="100" /></span></span><b><a href="/wiki/WikiProject:%E6%95%B0%E5%AD%A6" title="WikiProject:数学">专题</a></b></li></ul> </div></td></tr></tbody></table></div> <div class="navbox-styles"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84261037"></div><div role="navigation" class="navbox" aria-labelledby="计算机科学的主要领域" style="padding:3px"><table class="nowraplinks hlist mw-collapsible mw-collapsed navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th scope="col" class="collapsible-title navbox-title" colspan="2"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84265675"><link rel="mw-deduplicated-inline-style" href="mw-data:TemplateStyles:r84244141"><div class="navbar plainlinks hlist navbar-mini"><ul><li class="nv-view"><a href="/wiki/Template:%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="Template:電腦科學"><abbr title="查看该模板">查</abbr></a></li><li class="nv-talk"><a href="/wiki/Template_talk:%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="Template talk:電腦科學"><abbr title="讨论该模板">论</abbr></a></li><li class="nv-edit"><a href="/wiki/Special:%E7%BC%96%E8%BE%91%E9%A1%B5%E9%9D%A2/Template:%E9%9B%BB%E8%85%A6%E7%A7%91%E5%AD%B8" title="Special:编辑页面/Template:電腦科學"><abbr title="编辑该模板">编</abbr></a></li></ul></div><div id="计算机科学的主要领域" style="font-size:110%;margin:0 5em"><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%A7%91%E5%AD%A6" title="计算机科学">计算机科学</a>的主要领域</div></th></tr><tr><td class="navbox-abovebelow" colspan="2"><div>注：该模板大致遵循<a href="/wiki/ACM_%E7%94%B5%E8%84%91%E5%88%86%E7%B1%BB%E7%B3%BB%E7%BB%9F" title="ACM 电脑分类系统">ACM 电脑分类系统</a>。</div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%A1%AC%E4%BB%B6" title="计算机硬件">计算机硬件</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%8D%B0%E5%88%B7%E7%94%B5%E8%B7%AF%E6%9D%BF" class="mw-redirect" title="印刷电路板">印刷电路板</a></li> <li><a href="/wiki/%E5%A4%96%E9%83%A8%E8%AE%BE%E5%A4%87" title="外部设备">外部设备</a></li> <li><a href="/wiki/%E9%9B%86%E6%88%90%E7%94%B5%E8%B7%AF" title="集成电路">集成电路</a></li> <li><a href="/wiki/%E8%B6%85%E5%A4%A7%E8%A7%84%E6%A8%A1%E9%9B%86%E6%88%90%E7%94%B5%E8%B7%AF" title="超大规模集成电路">超大规模集成电路</a></li> <li><a href="/wiki/%E7%BB%BF%E8%89%B2%E8%AE%A1%E7%AE%97" title="绿色计算">绿色计算</a></li> <li><a href="/wiki/%E9%9B%BB%E5%AD%90%E8%A8%AD%E8%A8%88%E8%87%AA%E5%8B%95%E5%8C%96" title="電子設計自動化">電子設計自動化</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%B3%BB%E7%BB%9F%E6%9E%B6%E6%9E%84" title="系统架构">系统架构</a>组织</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%B3%BB%E7%BB%9F%E7%BB%93%E6%9E%84" title="计算机系统结构">電腦系統架構</a></li> <li><a href="/wiki/%E5%B5%8C%E5%85%A5%E5%BC%8F%E7%B3%BB%E7%BB%9F" title="嵌入式系统">嵌入式系统</a></li> <li><a href="/wiki/%E5%AE%9E%E6%97%B6%E8%AE%A1%E7%AE%97" title="实时计算">实时计算</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E7%BD%91%E7%BB%9C" title="计算机网络">网络</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%BD%91%E7%BB%9C%E4%BC%A0%E8%BE%93%E5%8D%8F%E8%AE%AE" class="mw-redirect" title="网络传输协议">网络传输协议</a></li> <li><a href="/wiki/%E8%B7%AF%E7%94%B1" title="路由">路由</a></li> <li><a href="/wiki/%E7%BD%91%E7%BB%9C%E6%8B%93%E6%89%91" title="网络拓扑">网络拓扑</a></li> <li><a href="/wiki/%E7%BD%91%E7%BB%9C%E6%9C%8D%E5%8A%A1" class="mw-redirect" title="网络服务">网络服务</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">软件组织</th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9B%B4%E8%AD%AF%E5%99%A8" title="直譯器">直譯器</a></li> <li><a href="/wiki/%E4%B8%AD%E9%97%B4%E4%BB%B6" title="中间件">中间件</a></li> <li><a href="/wiki/%E8%99%9B%E6%93%AC%E6%A9%9F%E5%99%A8" title="虛擬機器">虛擬機器</a></li> <li><a href="/wiki/%E6%93%8D%E4%BD%9C%E7%B3%BB%E7%BB%9F" title="操作系统">操作系统</a></li> <li><a href="/wiki/%E8%BD%AF%E4%BB%B6%E8%B4%A8%E9%87%8F" title="软件质量">软件质量</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%A8%8B%E5%BC%8F%E8%AA%9E%E8%A8%80%E7%90%86%E8%AB%96" title="程式語言理論">软件符号</a>和<a href="/wiki/%E8%BD%AF%E4%BB%B6%E5%BC%80%E5%8F%91%E5%B7%A5%E5%85%B7" title="软件开发工具">工具</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%BC%96%E7%A8%8B%E8%8C%83%E5%9E%8B" title="编程范型">编程范型</a></li> <li><a href="/wiki/%E7%BC%96%E7%A8%8B%E8%AF%AD%E8%A8%80" title="编程语言">编程语言</a></li> <li><a href="/wiki/%E7%B7%A8%E8%AD%AF%E5%99%A8" title="編譯器">編譯器</a></li> <li><a href="/wiki/%E9%A2%86%E5%9F%9F%E7%89%B9%E5%AE%9A%E8%AF%AD%E8%A8%80" title="领域特定语言">领域特定语言</a></li> <li><a href="/wiki/%E8%BB%9F%E9%AB%94%E6%A1%86%E6%9E%B6" title="軟體框架">軟體框架</a></li> <li><a href="/wiki/%E9%9B%86%E6%88%90%E5%BC%80%E5%8F%91%E7%8E%AF%E5%A2%83" title="集成开发环境">集成开发环境</a></li> <li><a href="/wiki/%E8%BD%AF%E4%BB%B6%E9%85%8D%E7%BD%AE%E7%AE%A1%E7%90%86" title="软件配置管理">软件配置管理</a></li> <li><a href="/wiki/%E5%87%BD%E5%BC%8F%E5%BA%AB" title="函式庫">函式庫</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%BD%AF%E4%BB%B6%E5%BC%80%E5%8F%91" title="软件开发">软件开发</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%BD%AF%E4%BB%B6%E5%BC%80%E5%8F%91%E8%BF%87%E7%A8%8B" title="软件开发过程">软件开发过程</a></li> <li><a href="/wiki/%E9%9C%80%E6%B1%82%E5%88%86%E6%9E%90" title="需求分析">需求分析</a></li> <li><a href="/wiki/%E8%BD%AF%E4%BB%B6%E8%AE%BE%E8%AE%A1" title="软件设计">软件设计</a></li> <li><a href="/wiki/%E8%BD%AF%E4%BB%B6%E9%83%A8%E7%BD%B2" title="软件部署">软件部署</a></li> <li><a href="/wiki/%E8%BB%9F%E9%AB%94%E7%B6%AD%E8%AD%B7" title="軟體維護">軟體維護</a></li> <li><a href="/wiki/%E5%BC%80%E6%BA%90%E8%BD%AF%E4%BB%B6" title="开源软件">开源模式</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%AE%A1%E7%AE%97%E7%90%86%E8%AE%BA" title="计算理论">计算理论</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%87%AA%E5%8A%A8%E6%9C%BA" class="mw-redirect" title="自动机">自动机</a></li> <li><a href="/wiki/%E5%8F%AF%E8%AE%A1%E7%AE%97%E6%80%A7" title="可计算性">可计算性理论</a></li> <li><a href="/wiki/%E8%A8%88%E7%AE%97%E8%A4%87%E9%9B%9C%E6%80%A7%E7%90%86%E8%AB%96" title="計算複雜性理論">計算複雜性理論</a></li> <li><a href="/wiki/%E9%87%8F%E5%AD%90%E8%AE%A1%E7%AE%97%E6%9C%BA" title="量子计算机">量子计算</a></li> <li><a href="/wiki/%E6%95%B0%E5%80%BC%E5%88%86%E6%9E%90" title="数值分析">数值计算方法</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E9%80%BB%E8%BE%91" title="计算机逻辑">计算机逻辑</a></li> <li><a href="/wiki/%E5%BD%A2%E5%BC%8F%E8%AF%AD%E4%B9%89%E5%AD%A6" title="形式语义学">形式语义学</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E7%AE%97%E6%B3%95" title="算法">算法</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%AE%97%E6%B3%95%E5%88%86%E6%9E%90" title="算法分析">算法分析</a></li> <li><a href="/wiki/%E7%AE%97%E6%B3%95%E8%AE%BE%E8%AE%A1" title="算法设计">算法设计</a></li> <li><a href="/wiki/%E7%AE%97%E6%B3%95%E6%95%88%E7%8E%87" title="算法效率">算法效率</a></li> <li><a href="/wiki/%E9%9A%8F%E6%9C%BA%E5%8C%96%E7%AE%97%E6%B3%95" title="随机化算法">随机化算法</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E5%87%A0%E4%BD%95" title="计算几何">计算几何</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%">计算数学</th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%A6%BB%E6%95%A3%E6%95%B0%E5%AD%A6" title="离散数学">离散数学</a></li> <li><a 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style="width:1%"><a href="/wiki/%E4%BF%A1%E6%81%AF%E7%B3%BB%E7%BB%9F" title="信息系统">信息系统</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E6%95%B0%E6%8D%AE%E5%BA%93%E7%AE%A1%E7%90%86%E7%B3%BB%E7%BB%9F" title="数据库管理系统">数据库管理系统</a></li> <li><a href="/wiki/%E9%9B%BB%E8%85%A6%E6%95%B8%E6%93%9A%E5%AD%98%E8%B2%AF%E5%99%A8" class="mw-redirect" title="電腦數據存貯器">電腦數據</a></li> <li><a href="/w/index.php?title=%E4%BC%81%E4%B8%9A%E4%BF%A1%E6%81%AF%E7%B3%BB%E7%BB%9F&action=edit&redlink=1" class="new" title="企业信息系统（页面不存在）">企业信息系统</a></li> <li><a href="/wiki/%E7%A4%BE%E4%BC%9A%E6%80%A7%E8%BD%AF%E4%BB%B6" title="社会性软件">社会性软件</a></li> <li><a href="/wiki/%E5%9C%B0%E7%90%86%E4%BF%A1%E6%81%AF%E7%B3%BB%E7%BB%9F" title="地理信息系统">地理信息系统</a></li> <li><a href="/wiki/%E5%86%B3%E7%AD%96%E6%94%AF%E6%8C%81%E7%B3%BB%E7%BB%9F" title="决策支持系统">决策支持系统</a></li> <li><a href="/wiki/%E8%BF%87%E7%A8%8B%E6%8E%A7%E5%88%B6" title="过程控制">过程控制</a></li> <li><a href="/wiki/%E6%95%B0%E6%8D%AE%E6%8C%96%E6%8E%98" title="数据挖掘">数据挖掘</a></li> <li><a href="/wiki/%E6%95%B8%E4%BD%8D%E5%9C%96%E6%9B%B8%E9%A4%A8" title="數位圖書館">數位圖書館</a></li> <li><a href="/wiki/%E7%B3%BB%E7%BB%9F%E5%B9%B3%E5%8F%B0" title="系统平台">系统平台</a></li> <li><a href="/wiki/%E6%95%B8%E4%BD%8D%E8%A1%8C%E9%8A%B7" title="數位行銷">數位行銷</a></li> <li><a href="/wiki/%E4%B8%87%E7%BB%B4%E7%BD%91" title="万维网">万维网</a></li> <li><a href="/wiki/%E4%BF%A1%E6%81%AF%E6%AA%A2%E7%B4%A2" title="信息檢索">信息檢索</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E5%AE%89%E5%85%A8" title="计算机安全">安全</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E5%AF%86%E7%A0%81%E5%AD%A6" title="密码学">密码学</a></li> <li><a href="/wiki/%E5%BD%A2%E5%BC%8F%E5%8C%96%E6%96%B9%E6%B3%95" title="形式化方法">形式化方法</a></li> <li><a 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title="人工智能">人工智能</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%87%AA%E5%8A%A8%E6%8E%A8%E7%90%86" title="自动推理">自动推理</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E8%AF%AD%E8%A8%80%E5%AD%A6" title="计算语言学">计算语言学</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E8%A7%86%E8%A7%89" title="计算机视觉">计算机视觉</a></li> <li><a href="/wiki/%E8%BF%9B%E5%8C%96%E8%AE%A1%E7%AE%97" title="进化计算">进化计算</a></li> <li><a href="/wiki/%E4%B8%93%E5%AE%B6%E7%B3%BB%E7%BB%9F" title="专家系统">专家系统</a></li> <li><a href="/wiki/%E8%87%AA%E7%84%B6%E8%AF%AD%E8%A8%80%E5%A4%84%E7%90%86" title="自然语言处理">自然语言处理</a></li> <li><a href="/wiki/%E6%9C%BA%E5%99%A8%E4%BA%BA%E5%AD%A6" title="机器人学">机器人学</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E6%9C%BA%E5%99%A8%E5%AD%A6%E4%B9%A0" title="机器学习">机器学习</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E7%9B%91%E7%9D%A3%E5%AD%A6%E4%B9%A0" title="监督学习">監督式學習</a></li> <li><a href="/wiki/%E7%84%A1%E7%9B%A3%E7%9D%A3%E5%AD%B8%E7%BF%92" title="無監督學習">無監督學習</a></li> <li><a href="/wiki/%E5%BC%BA%E5%8C%96%E5%AD%A6%E4%B9%A0" title="强化学习">强化学习</a></li> <li><a href="/wiki/%E4%BA%A4%E5%8F%89%E9%A9%97%E8%AD%89" title="交叉驗證">交叉驗證</a></li></ul> </div></td></tr><tr><th scope="row" class="navbox-group" style="width:1%"><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E5%9B%BE%E5%BD%A2%E5%AD%A6" title="计算机图形学">计算机图形学</a></th><td class="navbox-list-with-group navbox-list navbox-even" style="width:100%;padding:0px"><div style="padding:0em 0.25em"> <ul><li><a href="/wiki/%E8%AE%A1%E7%AE%97%E6%9C%BA%E5%8A%A8%E7%94%BB" title="计算机动画">计算机动画</a></li> <li><a href="/wiki/%E5%8F%AF%E8%A7%86%E5%8C%96" title="可视化">可视化</a></li> <li><a href="/wiki/%E6%B8%B2%E6%9F%93" title="渲染">渲染</a></li> <li><a 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href="/wiki/%E8%AE%A1%E7%AE%97%E6%95%B0%E5%AD%A6" class="mw-redirect" title="计算数学">计算数学</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E7%89%A9%E7%90%86%E5%AD%A6" title="计算物理学">计算物理学</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E5%8C%96%E5%AD%A6" title="计算化学">计算化学</a></li> <li><a href="/wiki/%E8%AE%A1%E7%AE%97%E7%94%9F%E7%89%A9%E5%AD%A6" title="计算生物学">计算生物学</a></li> <li><a href="/wiki/%E8%A8%88%E7%AE%97%E7%A4%BE%E6%9C%83%E7%A7%91%E5%AD%B8" title="計算社會科學">計算社會科學</a></li> <li><a href="/wiki/%E5%8C%BB%E5%AD%A6%E4%BF%A1%E6%81%AF%E5%AD%A6" title="医学信息学">医学信息学</a></li> <li><a href="/wiki/%E6%95%B0%E5%AD%97%E8%89%BA%E6%9C%AF" title="数字艺术">数字艺术</a></li> <li><a href="/wiki/%E9%9B%BB%E5%AD%90%E5%87%BA%E7%89%88" title="電子出版">電子出版</a></li> <li><a href="/wiki/%E7%B6%B2%E7%B5%A1%E6%88%B0" title="網絡戰">網絡戰</a></li> <li><a href="/wiki/%E7%94%B5%E5%AD%90%E6%B8%B8%E6%88%8F" title="电子游戏">电子游戏</a></li> <li><a href="/wiki/%E6%96%87%E5%AD%97%E5%A4%84%E7%90%86%E5%99%A8" title="文字处理器">文字处理器</a></li> <li><a href="/wiki/%E9%81%8B%E7%B1%8C%E5%AD%B8" title="運籌學">運籌學</a></li> <li><a href="/wiki/%E6%95%99%E8%82%B2%E6%8A%80%E6%9C%AF%E5%AD%A6" class="mw-redirect" title="教育技术学">教育技术学</a></li> <li><a href="/wiki/%E7%94%9F%E7%89%A9%E4%BF%A1%E6%81%AF%E5%AD%A6" title="生物信息学">生物信息学</a></li> <li><a href="/wiki/%E8%AE%A4%E7%9F%A5%E7%A7%91%E5%AD%A6" title="认知科学">认知科学</a></li> <li><span class="ilh-all" data-orig-title="文件管理系统" data-lang-code="en" data-lang-name="英语" data-foreign-title="Document management system"><span class="ilh-page"><a href="/w/index.php?title=%E6%96%87%E4%BB%B6%E7%AE%A1%E7%90%86%E7%B3%BB%E7%BB%9F&action=edit&redlink=1" class="new" title="文件管理系统（页面不存在）">文件管理系统</a></span><span class="noprint ilh-comment">（<span class="ilh-lang">英语</span><span class="ilh-colon">：</span><span class="ilh-link"><a href="https://en.wikipedia.org/wiki/Document_management_system" class="extiw" title="en:Document management system"><span lang="en" dir="auto">Document management 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