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barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-main-menu.unpin">ezkutatu</button> </div> <div id="p-navigation" class="vector-menu mw-portlet mw-portlet-navigation" > <div class="vector-menu-heading"> Nabigazioa </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="n-mainpage" class="mw-list-item"><a href="/wiki/Azala" title="Azala bisitatu [z]" accesskey="z"><span>Azala</span></a></li><li id="n-Txikipedia" class="mw-list-item"><a href="/wiki/Txikipedia:Azala"><span>Txikipedia</span></a></li><li id="n-Ikusgela" class="mw-list-item"><a href="/wiki/Atari:Hezkuntza/Ikusgela"><span>Ikusgela</span></a></li><li id="n-portal" class="mw-list-item"><a href="/wiki/Wikipedia:Txokoa" title="Proiektuaren inguruan, zer egin dezakezu, non aurkitu nahi duzuna"><span>Txokoa</span></a></li><li id="n-recentchanges" class="mw-list-item"><a href="/wiki/Berezi:AzkenAldaketak" title="Wikiko azken aldaketen zerrenda. [r]" accesskey="r"><span>Aldaketa berriak</span></a></li><li id="n-randompage" class="mw-list-item"><a href="/wiki/Berezi:Ausazkoa" title="Ausazko orrialde bat kargatu [x]" accesskey="x"><span>Ausazko orria</span></a></li><li id="n-help" class="mw-list-item"><a href="/wiki/Laguntza:Sarrera" title="Aurkitzeko lekua."><span>Laguntza</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> <a href="/wiki/Azala" class="mw-logo"> <img class="mw-logo-icon" src="/static/images/icons/wikipedia.png" alt="" aria-hidden="true" height="50" width="50"> <span class="mw-logo-container skin-invert"> <img class="mw-logo-wordmark" alt="Wikipedia" src="/static/images/mobile/copyright/wikipedia-wordmark-en.svg" style="width: 7.5em; height: 1.125em;"> <img class="mw-logo-tagline" alt="Entziklopedia askea" src="/static/images/mobile/copyright/wikipedia-tagline-eu.svg" width="120" height="13" style="width: 7.5em; height: 0.8125em;"> </span> </a> </div> <div class="vector-header-end"> <div id="p-search" role="search" class="vector-search-box-vue vector-search-box-collapses vector-search-box-show-thumbnail vector-search-box-auto-expand-width vector-search-box"> <a href="/wiki/Berezi:Bilatu" class="cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet cdx-button--icon-only search-toggle" title="Wikipedia(e)n bilatu [f]" accesskey="f"><span class="vector-icon mw-ui-icon-search mw-ui-icon-wikimedia-search"></span> <span>Bilatu</span> </a> <div class="vector-typeahead-search-container"> <div class="cdx-typeahead-search cdx-typeahead-search--show-thumbnail cdx-typeahead-search--auto-expand-width"> <form action="/w/index.php" id="searchform" class="cdx-search-input cdx-search-input--has-end-button"> <div id="simpleSearch" class="cdx-search-input__input-wrapper" data-search-loc="header-moved"> <div class="cdx-text-input cdx-text-input--has-start-icon"> <input class="cdx-text-input__input" type="search" name="search" placeholder="Wikipedia wikian bilatu" aria-label="Wikipedia wikian bilatu" autocapitalize="sentences" title="Wikipedia(e)n bilatu [f]" accesskey="f" id="searchInput" > <span class="cdx-text-input__icon cdx-text-input__start-icon"></span> </div> <input type="hidden" name="title" value="Berezi:Bilatu"> </div> <button class="cdx-button cdx-search-input__end-button">Bilatu</button> </form> </div> </div> </div> <nav class="vector-user-links vector-user-links-wide" aria-label="Tresna pertsonalak"> <div class="vector-user-links-main"> <div id="p-vector-user-menu-preferences" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-userpage" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <nav class="vector-appearance-landmark" aria-label="Itxura"> <div id="vector-appearance-dropdown" class="vector-dropdown " title="Change the appearance of the page's font size, width, and color" > <input type="checkbox" id="vector-appearance-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-appearance-dropdown" class="vector-dropdown-checkbox " aria-label="Itxura" > <label id="vector-appearance-dropdown-label" for="vector-appearance-dropdown-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-appearance mw-ui-icon-wikimedia-appearance"></span> <span class="vector-dropdown-label-text">Itxura</span> </label> <div class="vector-dropdown-content"> <div id="vector-appearance-unpinned-container" class="vector-unpinned-container"> </div> </div> </div> </nav> <div id="p-vector-user-menu-notifications" class="vector-menu mw-portlet emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> <div id="p-vector-user-menu-overflow" class="vector-menu mw-portlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_eu.wikipedia.org&uselang=eu" class=""><span>Dohaintza egin</span></a> </li> <li id="pt-createaccount-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Berezi:KontuaSortu&returnto=Zenbakien+teoria" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea." class=""><span>Sortu kontua</span></a> </li> <li id="pt-login-2" class="user-links-collapsible-item mw-list-item user-links-collapsible-item"><a data-mw="interface" href="/w/index.php?title=Berezi:SaioaHasi&returnto=Zenbakien+teoria" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o" class=""><span>Hasi saioa</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown vector-user-menu vector-button-flush-right vector-user-menu-logged-out" title="Aukera gehiago" > <input type="checkbox" id="vector-user-links-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-user-links-dropdown" class="vector-dropdown-checkbox " aria-label="Tresna pertsonalak" > <label id="vector-user-links-dropdown-label" for="vector-user-links-dropdown-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-ellipsis mw-ui-icon-wikimedia-ellipsis"></span> <span class="vector-dropdown-label-text">Tresna pertsonalak</span> </label> <div class="vector-dropdown-content"> <div id="p-personal" class="vector-menu mw-portlet mw-portlet-personal user-links-collapsible-item" title="User menu" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="//donate.wikimedia.org/wiki/Special:FundraiserRedirector?utm_source=donate&utm_medium=sidebar&utm_campaign=C13_eu.wikipedia.org&uselang=eu"><span>Dohaintza egin</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:KontuaSortu&returnto=Zenbakien+teoria" title="Kontu bat sortu eta horrekin saioa hastea eskatu nahi genizuke; ez da ezinbestekoa, ordea."><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>Sortu kontua</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=Berezi:SaioaHasi&returnto=Zenbakien+teoria" title="Izen ematera gonbidatzen zaitugu. [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>Hasi saioa</span></a></li> </ul> </div> </div> <div id="p-user-menu-anon-editor" class="vector-menu mw-portlet mw-portlet-user-menu-anon-editor" > <div class="vector-menu-heading"> Izena eman gabeko erabiltzaileentzako orrialdeak <a href="/wiki/Laguntza:Sarrera" aria-label="Artikuluak aldatzeari buruz gehiago ikasi"><span>gehiago ikasi</span></a> </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="pt-anoncontribs" class="mw-list-item"><a href="/wiki/Berezi:NireEkarpenak" title="IP helbide honetatik egindako aldaketen zerrenda [y]" accesskey="y"><span>Ekarpenak</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/Berezi:NireEztabaida" title="Zure IParen eztabaida [n]" accesskey="n"><span>Eztabaida</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> </div> <div class="mw-page-container"> <div class="mw-page-container-inner"> <div class="vector-sitenotice-container"> <div id="siteNotice"></div> </div> <div class="vector-column-start"> <div class="vector-main-menu-container"> <div id="mw-navigation"> <nav id="mw-panel" class="vector-main-menu-landmark" aria-label="Gunea"> <div id="vector-main-menu-pinned-container" class="vector-pinned-container"> </div> </nav> </div> </div> <div class="vector-sticky-pinned-container"> <nav id="mw-panel-toc" aria-label="Edukiak" data-event-name="ui.sidebar-toc" class="mw-table-of-contents-container vector-toc-landmark"> <div id="vector-toc-pinned-container" class="vector-pinned-container"> <div id="vector-toc" class="vector-toc vector-pinnable-element"> <div class="vector-pinnable-header vector-toc-pinnable-header vector-pinnable-header-pinned" data-feature-name="toc-pinned" data-pinnable-element-id="vector-toc" > <h2 class="vector-pinnable-header-label">Edukiak</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">mugitu alboko barrara</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">ezkutatu</button> </div> <ul class="vector-toc-contents" id="mw-panel-toc-list"> <li id="toc-mw-content-text" class="vector-toc-list-item vector-toc-level-1"> <a href="#" class="vector-toc-link"> <div class="vector-toc-text">⇑ Gora</div> </a> </li> <li id="toc-Historia" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Historia"> <div class="vector-toc-text"> <span class="vector-toc-numb">1</span> <span>Historia</span> </div> </a> <button aria-controls="toc-Historia-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Historia azpiatal</span> </button> <ul id="toc-Historia-sublist" class="vector-toc-list"> <li id="toc-Jatorriak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Jatorriak"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1</span> <span>Jatorriak</span> </div> </a> <ul id="toc-Jatorriak-sublist" class="vector-toc-list"> <li id="toc-Aritmetikaren_jatorria" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Aritmetikaren_jatorria"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.1.1</span> <span>Aritmetikaren jatorria</span> </div> </a> <ul id="toc-Aritmetikaren_jatorria-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Zenbakien_teoria_modernoa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbakien_teoria_modernoa"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2</span> <span>Zenbakien teoria modernoa</span> </div> </a> <ul id="toc-Zenbakien_teoria_modernoa-sublist" class="vector-toc-list"> <li id="toc-Fermat" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Fermat"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.1</span> <span>Fermat</span> </div> </a> <ul id="toc-Fermat-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Euler" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Euler"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.2</span> <span>Euler</span> </div> </a> <ul id="toc-Euler-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Lagrange" class="vector-toc-list-item vector-toc-level-3"> <a class="vector-toc-link" href="#Lagrange"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.2.3</span> <span>Lagrange</span> </div> </a> <ul id="toc-Lagrange-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Izaeraren_eta_azpieremuen_sorrera" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Izaeraren_eta_azpieremuen_sorrera"> <div class="vector-toc-text"> <span class="vector-toc-numb">1.3</span> <span>Izaeraren eta azpieremuen sorrera</span> </div> </a> <ul id="toc-Izaeraren_eta_azpieremuen_sorrera-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Azpiatal_nagusiak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Azpiatal_nagusiak"> <div class="vector-toc-text"> <span class="vector-toc-numb">2</span> <span>Azpiatal nagusiak</span> </div> </a> <button aria-controls="toc-Azpiatal_nagusiak-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Azpiatal nagusiak azpiatal</span> </button> <ul id="toc-Azpiatal_nagusiak-sublist" class="vector-toc-list"> <li id="toc-Tresna_elementalak" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Tresna_elementalak"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.1</span> <span>Tresna elementalak</span> </div> </a> <ul id="toc-Tresna_elementalak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbakien_teoria_analitikoa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbakien_teoria_analitikoa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.2</span> <span>Zenbakien teoria analitikoa</span> </div> </a> <ul id="toc-Zenbakien_teoria_analitikoa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbakien_teoria_aljebraikoa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbakien_teoria_aljebraikoa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.3</span> <span>Zenbakien teoria aljebraikoa</span> </div> </a> <ul id="toc-Zenbakien_teoria_aljebraikoa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Geometria_Diofantikoa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Geometria_Diofantikoa"> <div class="vector-toc-text"> <span class="vector-toc-numb">2.4</span> <span>Geometria Diofantikoa</span> </div> </a> <ul id="toc-Geometria_Diofantikoa-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Beste_eremu_batzuk" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Beste_eremu_batzuk"> <div class="vector-toc-text"> <span class="vector-toc-numb">3</span> <span>Beste eremu batzuk</span> </div> </a> <button aria-controls="toc-Beste_eremu_batzuk-sublist" class="cdx-button cdx-button--weight-quiet cdx-button--icon-only vector-toc-toggle"> <span class="vector-icon mw-ui-icon-wikimedia-expand"></span> <span>Erakutsi/ezkutatu Beste eremu batzuk azpiatal</span> </button> <ul id="toc-Beste_eremu_batzuk-sublist" class="vector-toc-list"> <li id="toc-Konbinatoria_aritmetikoa" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Konbinatoria_aritmetikoa"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.1</span> <span>Konbinatoria aritmetikoa</span> </div> </a> <ul id="toc-Konbinatoria_aritmetikoa-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Zenbaki-teoria_konputazionala" class="vector-toc-list-item vector-toc-level-2"> <a class="vector-toc-link" href="#Zenbaki-teoria_konputazionala"> <div class="vector-toc-text"> <span class="vector-toc-numb">3.2</span> <span>Zenbaki-teoria konputazionala</span> </div> </a> <ul id="toc-Zenbaki-teoria_konputazionala-sublist" class="vector-toc-list"> </ul> </li> </ul> </li> <li id="toc-Aplikazioak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Aplikazioak"> <div class="vector-toc-text"> <span class="vector-toc-numb">4</span> <span>Aplikazioak</span> </div> </a> <ul id="toc-Aplikazioak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Erreferentziak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Erreferentziak"> <div class="vector-toc-text"> <span class="vector-toc-numb">5</span> <span>Erreferentziak</span> </div> </a> <ul id="toc-Erreferentziak-sublist" class="vector-toc-list"> </ul> </li> <li id="toc-Kanpo_estekak" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#Kanpo_estekak"> <div class="vector-toc-text"> <span class="vector-toc-numb">6</span> <span>Kanpo estekak</span> </div> </a> <ul id="toc-Kanpo_estekak-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="Edukiak" 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="Eduki taularen ikusgarritasuna aldatu" > <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">Eduki taularen ikusgarritasuna aldatu</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">Zenbakien teoria</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="Joan beste hizkuntza batean idatzitako artikulu batera. 114 hizkuntzatan eskuragarri." > <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 hizkuntza</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 – afrikaansa" lang="af" hreflang="af" data-title="Getalteorie" data-language-autonym="Afrikaans" data-language-local-name="afrikaansa" 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 – Suitzako alemana" lang="gsw" hreflang="gsw" data-title="Zahlentheorie" data-language-autonym="Alemannisch" data-language-local-name="Suitzako alemana" 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 – aragoiera" lang="an" hreflang="an" data-title="Teoría de numeros" data-language-autonym="Aragonés" data-language-local-name="aragoiera" 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 – arabiera" lang="ar" hreflang="ar" data-title="نظرية الأعداد" data-language-autonym="العربية" data-language-local-name="arabiera" 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 – Moroccan Arabic" lang="ary" hreflang="ary" data-title="نضرية د لأعداد" data-language-autonym="الدارجة" data-language-local-name="Moroccan Arabic" 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 – Egyptian Arabic" lang="arz" hreflang="arz" data-title="نظريه الاعداد" data-language-autonym="مصرى" data-language-local-name="Egyptian Arabic" 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 – assamera" lang="as" hreflang="as" data-title="সংখ্যাতত্ত্ব" data-language-autonym="অসমীয়া" data-language-local-name="assamera" 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 – asturiera" lang="ast" hreflang="ast" data-title="Teoría de númberos" data-language-autonym="Asturianu" data-language-local-name="asturiera" 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 – azerbaijanera" lang="az" hreflang="az" data-title="Ədədlər nəzəriyyəsi" data-language-autonym="Azərbaycanca" data-language-local-name="azerbaijanera" 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 – baxkirera" lang="ba" hreflang="ba" data-title="Һандар теорияһы" data-language-autonym="Башҡортса" data-language-local-name="baxkirera" 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 – Samogitian" lang="sgs" hreflang="sgs" data-title="Skaitliu teuorėjė" data-language-autonym="Žemaitėška" data-language-local-name="Samogitian" 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 – bielorrusiera" lang="be" hreflang="be" data-title="Тэорыя лікаў" data-language-autonym="Беларуская" data-language-local-name="bielorrusiera" 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 – bulgariera" lang="bg" hreflang="bg" data-title="Теория на числата" data-language-autonym="Български" data-language-local-name="bulgariera" 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 – bengalera" lang="bn" hreflang="bn" data-title="সংখ্যাতত্ত্ব" data-language-autonym="বাংলা" data-language-local-name="bengalera" 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 – bretoiera" lang="br" hreflang="br" data-title="Damkaniezh an niveroù" data-language-autonym="Brezhoneg" data-language-local-name="bretoiera" 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 – bosniera" lang="bs" hreflang="bs" data-title="Teorija brojeva" data-language-autonym="Bosanski" data-language-local-name="bosniera" 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 – katalana" lang="ca" hreflang="ca" data-title="Teoria de nombres" data-language-autonym="Català" data-language-local-name="katalana" 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 – erdialdeko kurduera" lang="ckb" hreflang="ckb" data-title="تیۆریی ژمارە" data-language-autonym="کوردی" data-language-local-name="erdialdeko kurduera" 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 – txekiera" lang="cs" hreflang="cs" data-title="Teorie čísel" data-language-autonym="Čeština" data-language-local-name="txekiera" 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 – txuvaxera" lang="cv" hreflang="cv" data-title="Хисепсен теорийĕ" data-language-autonym="Чӑвашла" data-language-local-name="txuvaxera" 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 – galesa" lang="cy" hreflang="cy" data-title="Damcaniaeth rhifau" data-language-autonym="Cymraeg" data-language-local-name="galesa" 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 – daniera" lang="da" hreflang="da" data-title="Talteori" data-language-autonym="Dansk" data-language-local-name="daniera" 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 – alemana" lang="de" hreflang="de" data-title="Zahlentheorie" data-language-autonym="Deutsch" data-language-local-name="alemana" 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 – greziera" lang="el" hreflang="el" data-title="Θεωρία αριθμών" data-language-autonym="Ελληνικά" data-language-local-name="greziera" 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 – ingelesa" lang="en" hreflang="en" data-title="Number theory" data-language-autonym="English" data-language-local-name="ingelesa" 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 – esperantoa" lang="eo" hreflang="eo" data-title="Nombroteorio" data-language-autonym="Esperanto" data-language-local-name="esperantoa" 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 – gaztelania" lang="es" hreflang="es" data-title="Teoría de números" data-language-autonym="Español" data-language-local-name="gaztelania" 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 – estoniera" lang="et" hreflang="et" data-title="Arvuteooria" data-language-autonym="Eesti" data-language-local-name="estoniera" class="interlanguage-link-target"><span>Eesti</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 – persiera" lang="fa" hreflang="fa" data-title="نظریه اعداد" data-language-autonym="فارسی" data-language-local-name="persiera" 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 – finlandiera" lang="fi" hreflang="fi" data-title="Lukuteoria" data-language-autonym="Suomi" data-language-local-name="finlandiera" 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 – Võro" lang="vro" hreflang="vro" data-title="Arvoteooria" data-language-autonym="Võro" data-language-local-name="Võro" 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 – fijiera" lang="fj" hreflang="fj" data-title="Naba icavacava" data-language-autonym="Na Vosa Vakaviti" data-language-local-name="fijiera" 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 – frantsesa" lang="fr" hreflang="fr" data-title="Théorie des nombres" data-language-autonym="Français" data-language-local-name="frantsesa" 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 – iparraldeko frisiera" lang="frr" hreflang="frr" data-title="Taalenteorii" data-language-autonym="Nordfriisk" data-language-local-name="iparraldeko frisiera" 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 – irlandera" lang="ga" hreflang="ga" data-title="Uimhirtheoiric" data-language-autonym="Gaeilge" data-language-local-name="irlandera" 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 – Gan" lang="gan" hreflang="gan" data-title="數論" data-language-autonym="贛語" data-language-local-name="Gan" 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 – galiziera" lang="gl" hreflang="gl" data-title="Teoría de números" data-language-autonym="Galego" data-language-local-name="galiziera" 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 – gujaratera" lang="gu" hreflang="gu" data-title="સંખ્યા સિદ્ધાંત" data-language-autonym="ગુજરાતી" data-language-local-name="gujaratera" 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 – hebreera" lang="he" hreflang="he" data-title="תורת המספרים" data-language-autonym="עברית" data-language-local-name="hebreera" 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 – hindia" lang="hi" hreflang="hi" data-title="संख्या सिद्धान्त" data-language-autonym="हिन्दी" data-language-local-name="hindia" 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 – Fiji Hindi" lang="hif" hreflang="hif" data-title="Number theory" data-language-autonym="Fiji Hindi" data-language-local-name="Fiji Hindi" 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 – kroaziera" lang="hr" hreflang="hr" data-title="Teorija brojeva" data-language-autonym="Hrvatski" data-language-local-name="kroaziera" 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 – hungariera" lang="hu" hreflang="hu" data-title="Számelmélet" data-language-autonym="Magyar" data-language-local-name="hungariera" 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 – armeniera" lang="hy" hreflang="hy" data-title="Թվերի տեսություն" data-language-autonym="Հայերեն" data-language-local-name="armeniera" 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 – interlingua" lang="ia" hreflang="ia" data-title="Theoria de numeros" data-language-autonym="Interlingua" data-language-local-name="interlingua" 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 – indonesiera" lang="id" hreflang="id" data-title="Teori bilangan" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonesiera" 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 – idoa" lang="io" hreflang="io" data-title="Teorio di nombri" data-language-autonym="Ido" data-language-local-name="idoa" 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 – islandiera" lang="is" hreflang="is" data-title="Talnafræði" data-language-autonym="Íslenska" data-language-local-name="islandiera" 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 – italiera" lang="it" hreflang="it" data-title="Teoria dei numeri" data-language-autonym="Italiano" data-language-local-name="italiera" 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 – japoniera" lang="ja" hreflang="ja" data-title="数論" data-language-autonym="日本語" data-language-local-name="japoniera" 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 – Jamaican Creole English" lang="jam" hreflang="jam" data-title="Nomba tiori" data-language-autonym="Patois" data-language-local-name="Jamaican Creole English" 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 – lojbana" lang="jbo" hreflang="jbo" data-title="nacycmaci" data-language-autonym="La .lojban." data-language-local-name="lojbana" 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 – javera" lang="jv" hreflang="jv" data-title="Téori wilangan" data-language-autonym="Jawa" data-language-local-name="javera" 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 – georgiera" lang="ka" hreflang="ka" data-title="რიცხვთა თეორია" data-language-autonym="ქართული" data-language-local-name="georgiera" 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 – kazakhera" lang="kk" hreflang="kk" data-title="Сандар теориясы" data-language-autonym="Қазақша" data-language-local-name="kazakhera" 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 – kannada" lang="kn" hreflang="kn" data-title="ಸಂಖ್ಯಾಸಿದ್ಧಾಂತ" data-language-autonym="ಕನ್ನಡ" data-language-local-name="kannada" 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 – koreera" lang="ko" hreflang="ko" data-title="수론" data-language-autonym="한국어" data-language-local-name="koreera" 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 – kurduera" lang="ku" hreflang="ku" data-title="Bîrdoza jimare" data-language-autonym="Kurdî" data-language-local-name="kurduera" class="interlanguage-link-target"><span>Kurdî</span></a></li><li class="interlanguage-link interwiki-la badge-Q17437796 badge-featuredarticle mw-list-item" title="artikulu nabarmenduak"><a href="https://la.wikipedia.org/wiki/Theoria_numerorum" title="Theoria numerorum – latina" lang="la" hreflang="la" data-title="Theoria numerorum" data-language-autonym="Latina" data-language-local-name="latina" 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 – luxenburgera" lang="lb" hreflang="lb" data-title="Zuelentheorie" data-language-autonym="Lëtzebuergesch" data-language-local-name="luxenburgera" 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 – Lombard" lang="lmo" hreflang="lmo" data-title="Teoria di numer" data-language-autonym="Lombard" data-language-local-name="Lombard" 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 – lituaniera" lang="lt" hreflang="lt" data-title="Skaičių teorija" data-language-autonym="Lietuvių" data-language-local-name="lituaniera" 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 – letoniera" lang="lv" hreflang="lv" data-title="Skaitļu teorija" data-language-autonym="Latviešu" data-language-local-name="letoniera" 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 – mazedoniera" lang="mk" hreflang="mk" data-title="Теорија на броевите" data-language-autonym="Македонски" data-language-local-name="mazedoniera" 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 – malabarera" lang="ml" hreflang="ml" data-title="സംഖ്യാസിദ്ധാന്തം" data-language-autonym="മലയാളം" data-language-local-name="malabarera" 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 – mongoliera" lang="mn" hreflang="mn" data-title="Тооны онол" data-language-autonym="Монгол" data-language-local-name="mongoliera" 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 – marathera" lang="mr" hreflang="mr" data-title="अंकशास्त्र" data-language-autonym="मराठी" data-language-local-name="marathera" 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 – malaysiera" lang="ms" hreflang="ms" data-title="Teori nombor" data-language-autonym="Bahasa Melayu" data-language-local-name="malaysiera" 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 – maltera" lang="mt" hreflang="mt" data-title="Teorija tan-numri" data-language-autonym="Malti" data-language-local-name="maltera" 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 – birmaniera" lang="my" hreflang="my" data-title="ကိန်းသီအိုရီ" data-language-autonym="မြန်မာဘာသာ" data-language-local-name="birmaniera" 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 – behe-alemana" lang="nds" hreflang="nds" data-title="Tallentheorie" data-language-autonym="Plattdüütsch" data-language-local-name="behe-alemana" 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 – nederlandera" lang="nl" hreflang="nl" data-title="Getaltheorie" data-language-autonym="Nederlands" data-language-local-name="nederlandera" 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 – nynorsk (norvegiera)" lang="nn" hreflang="nn" data-title="Talteori" data-language-autonym="Norsk nynorsk" data-language-local-name="nynorsk (norvegiera)" 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 – bokmål (norvegiera)" lang="nb" hreflang="nb" data-title="Tallteori" data-language-autonym="Norsk bokmål" data-language-local-name="bokmål (norvegiera)" 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 – okzitaniera" lang="oc" hreflang="oc" data-title="Teoria dels nombres" data-language-autonym="Occitan" data-language-local-name="okzitaniera" 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 – punjabera" lang="pa" hreflang="pa" data-title="ਅੰਕ ਸਿਧਾਂਤ" data-language-autonym="ਪੰਜਾਬੀ" data-language-local-name="punjabera" 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 – poloniera" lang="pl" hreflang="pl" data-title="Teoria liczb" data-language-autonym="Polski" data-language-local-name="poloniera" 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 – Piedmontese" lang="pms" hreflang="pms" data-title="Teorìa dij nùmer" data-language-autonym="Piemontèis" data-language-local-name="Piedmontese" 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 – portugesa" lang="pt" hreflang="pt" data-title="Teoria dos números" data-language-autonym="Português" data-language-local-name="portugesa" 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 – errumaniera" lang="ro" hreflang="ro" data-title="Teoria numerelor" data-language-autonym="Română" data-language-local-name="errumaniera" 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 – errusiera" lang="ru" hreflang="ru" data-title="Теория чисел" data-language-autonym="Русский" data-language-local-name="errusiera" 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 – sanskritoa" lang="sa" hreflang="sa" data-title="संख्याशास्त्रम्" data-language-autonym="संस्कृतम्" data-language-local-name="sanskritoa" 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 – sakhera" lang="sah" hreflang="sah" data-title="Саамай улахан уопсай түҥэтээччи" data-language-autonym="Саха тыла" data-language-local-name="sakhera" 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 – siziliera" lang="scn" hreflang="scn" data-title="Tiurìa dî nùmmura" data-language-autonym="Sicilianu" data-language-local-name="siziliera" 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 – eskoziera" lang="sco" hreflang="sco" data-title="Nummer theory" data-language-autonym="Scots" data-language-local-name="eskoziera" 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 – serbokroaziera" lang="sh" hreflang="sh" data-title="Teorija brojeva" data-language-autonym="Srpskohrvatski / српскохрватски" data-language-local-name="serbokroaziera" 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 – eslovakiera" lang="sk" hreflang="sk" data-title="Teória čísel" data-language-autonym="Slovenčina" data-language-local-name="eslovakiera" 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 – esloveniera" lang="sl" hreflang="sl" data-title="Teorija števil" data-language-autonym="Slovenščina" data-language-local-name="esloveniera" 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 – albaniera" lang="sq" hreflang="sq" data-title="Teoria e numrave" data-language-autonym="Shqip" data-language-local-name="albaniera" 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 – serbiera" lang="sr" hreflang="sr" data-title="Теорија бројева" data-language-autonym="Српски / srpski" data-language-local-name="serbiera" 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 – suediera" lang="sv" hreflang="sv" data-title="Talteori" data-language-autonym="Svenska" data-language-local-name="suediera" 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 – swahilia" lang="sw" hreflang="sw" data-title="Nadharia ya namba" data-language-autonym="Kiswahili" data-language-local-name="swahilia" 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 – tamilera" lang="ta" hreflang="ta" data-title="எண் கோட்பாடு" data-language-autonym="தமிழ்" data-language-local-name="tamilera" 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 – thailandiera" lang="th" hreflang="th" data-title="ทฤษฎีจำนวน" data-language-autonym="ไทย" data-language-local-name="thailandiera" 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 – turkmenera" lang="tk" hreflang="tk" data-title="Sanlar teoriýasy" data-language-autonym="Türkmençe" data-language-local-name="turkmenera" 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 – tagaloa" lang="tl" hreflang="tl" data-title="Teorya ng bilang" data-language-autonym="Tagalog" data-language-local-name="tagaloa" 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 – turkiera" lang="tr" hreflang="tr" data-title="Sayılar teorisi" data-language-autonym="Türkçe" data-language-local-name="turkiera" 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 – ukrainera" lang="uk" hreflang="uk" data-title="Теорія чисел" data-language-autonym="Українська" data-language-local-name="ukrainera" 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 – urdua" lang="ur" hreflang="ur" data-title="نظریۂ عدد" data-language-autonym="اردو" data-language-local-name="urdua" 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 – uzbekera" lang="uz" hreflang="uz" data-title="Sonlar nazariyasi" data-language-autonym="Oʻzbekcha / ўзбекча" data-language-local-name="uzbekera" 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 – vietnamera" lang="vi" hreflang="vi" data-title="Lý thuyết số" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamera" 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 – volapük" lang="vo" hreflang="vo" data-title="Numateor" data-language-autonym="Volapük" data-language-local-name="volapük" 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 – warayera" lang="war" hreflang="war" data-title="Teyorya hin ihap" data-language-autonym="Winaray" data-language-local-name="warayera" 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 – wu txinera" lang="wuu" hreflang="wuu" data-title="数论" data-language-autonym="吴语" data-language-local-name="wu txinera" 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 – Mingrelian" lang="xmf" hreflang="xmf" data-title="რიცხუეფიშ თეორია" data-language-autonym="მარგალური" data-language-local-name="Mingrelian" 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 – yiddisha" lang="yi" hreflang="yi" data-title="נומערן טעאריע" data-language-autonym="ייִדיש" data-language-local-name="yiddisha" class="interlanguage-link-target"><span>ייִדיש</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E6%95%B0%E8%AE%BA" title="数论 – txinera" lang="zh" hreflang="zh" data-title="数论" data-language-autonym="中文" data-language-local-name="txinera" class="interlanguage-link-target"><span>中文</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 – Minnan" lang="nan" hreflang="nan" data-title="Sò͘-lūn" data-language-autonym="閩南語 / Bân-lâm-gú" data-language-local-name="Minnan" 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 – kantonera" lang="yue" hreflang="yue" data-title="數論" data-language-autonym="粵語" data-language-local-name="kantonera" 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="Aldatu hizkuntzen arteko loturak" class="wbc-editpage">Aldatu loturak</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="Izen-tarteak"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul 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href="/wiki/Wikipedia:Wikipedia_guztiek_izan_beharreko_artikuluen_zerrenda/3._maila" title="Artikulu hau Wikipedia guztiek izan beharreko artikuluen zerrendaren parte da"><img alt="Artikulu hau Wikipedia guztiek izan beharreko artikuluen zerrendaren parte da" src="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikipedia-1000.png/20px-Wikipedia-1000.png" decoding="async" width="20" height="18" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikipedia-1000.png/30px-Wikipedia-1000.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/9/91/Wikipedia-1000.png/40px-Wikipedia-1000.png 2x" data-file-width="1122" data-file-height="1024" /></a></span></div></div> </div> <div id="siteSub" class="noprint">Wikipedia, Entziklopedia askea</div> </div> <div id="contentSub"><div id="mw-content-subtitle"></div></div> <div id="mw-content-text" class="mw-body-content"><div class="mw-content-ltr mw-parser-output" lang="eu" dir="ltr"><p> <b>Zenbaki-teoria</b> (edo zenbakien teoria, edo goi mailako aritmetika) matematika puruaren adar bat da, zenbaki osoak eta zenbaki osoetako funtzioetan sakontzen gehienbat.  <a href="/wiki/Carl_Friedrich_Gauss" title="Carl Friedrich Gauss">Carl Friedrich Gauss</a> matematikari alemaniarrak honela zioen: “Matematika zientzien erregea da, eta zenbaki-teoria matematikaren erregea da”.<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> Zenbaki-teorian lan egiten duten zientzialariek zenbaki lehenak, zenbaki osoetatik eratorritako beste elementu matematiko batzuk (zenbaki arrazionalak, esaterako) eta zenbaki osoen orokorpenak aztertzen dituzte. </p> <meta property="mw:PageProp/toc" /> <div class="mw-heading mw-heading2"><h2 id="Historia">Historia</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=1" title="Aldatu atal hau: «Historia»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=1" title="Edit section's source code: Historia"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Jatorriak">Jatorriak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=2" title="Aldatu atal hau: «Jatorriak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=2" title="Edit section's source code: Jatorriak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Aritmetikaren_jatorria">Aritmetikaren jatorria</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=3" title="Aldatu atal hau: «Aritmetikaren jatorria»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=3" title="Edit section's source code: Aritmetikaren jatorria"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure class="mw-default-size" typeof="mw:File/Thumb"><a href="https://eu.wikipedia.org/wiki/Fitxategi:Plimpton_322.jpg"><img resource="/wiki/Fitxategi:Plimpton_322.jpg" src="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Plimpton_322.jpg/220px-Plimpton_322.jpg" decoding="async" width="220" height="152" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Plimpton_322.jpg/330px-Plimpton_322.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/c/c2/Plimpton_322.jpg/440px-Plimpton_322.jpg 2x" data-file-width="1246" data-file-height="863" /></a><figcaption>Plimpton<sup class="noprint Inline-Template"><span style="white-space: nowrap;">[<i><a href="/wiki/Wikipedia:Esteka_hautsia" class="mw-redirect" title="Wikipedia:Esteka hautsia"><span title=" Data honetatik dago hautsita esteka: martxoa 2021">Betiko hautsitako esteka</span></a></i>]</span></sup> 322 buztinezko taulatxoa</figcaption></figure> <p><a href="/wiki/Mesopotamia" title="Mesopotamia">Mesopotamia</a>ko <a href="/wiki/Larsa" title="Larsa">Larsa</a> hirian, K.a. 1800. urtean jatorria duen <a href="/w/index.php?title=Plinton_322&action=edit&redlink=1" class="new" title="Plinton 322 (sortu gabe)">Plinton 322</a> buztinezko taulatxoan ageri da historian lehen aldiz, aritmetikaren erabilera, non bertan <a href="/wiki/Pitagoras" title="Pitagoras">Pitagoras</a>en hirukoen zerrenda bat azaltzen den, hau da, <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}=c^{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> <mo>=</mo> <msup> <mi>c</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle a^{2}+b^{2}=c^{2}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/7ef0a5a4b8ab98870ae5d6d7c7b4dfe3fb6612e2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:12.336ex; height:2.843ex;" alt="{\displaystyle a^{2}+b^{2}=c^{2}}"></span> betetzen duten <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,b,c)}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo stretchy="false">(</mo> <mi>a</mi> <mo>,</mo> <mi>b</mi> <mo>,</mo> <mi>c</mi> <mo stretchy="false">)</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle (a,b,c)}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/ae973a762a92b9cd3eafe7f283890ccfa9b887e8" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.111ex; height:2.843ex;" alt="{\displaystyle (a,b,c)}"></span> zenbaki osoez osatutako tupla edo bektoreen zerrenda bat. Zerrenda hau seguruenik, garai hartako zenbait arazori irtenbidea aurkitzeko eta arazo horiek konpontzeko sortua izango zen. Babiloniar astronomian erabilera izan zezakeela uste da, eta beste iturri batzuen arabera, eskolako problemen zenbakizko adibideetan ere erabiltzen . </p><p>Nabarmentzekoa da zenbaki teoria <a href="/wiki/Babiloniar_Inperioa" title="Babiloniar Inperioa">babilonia</a>rra aljebra babiloniarrarekin alderatuta garatu gabea eta sinplea zela (aipaturiko lagina), azken hau bereziki garatua baitzegoen. </p><p><a href="/wiki/Eskola_pitagorikoa" title="Eskola pitagorikoa">Eskola pitagorikoa</a>k zenbakien izaera bikoitia sakon aztertu zuen. Zenbaki bakoiti batek, beste zenbaki bikoiti bat zatitzen badu, orduan honen erdia ere zatituko duenaren ideia abiapuntutzat hartuz, <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 {\sqrt {2}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <msqrt> <mn>2</mn> </msqrt> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\sqrt {2}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/b4afc1e27d418021bf10898eb44a7f5f315735ff" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.098ex; height:3.009ex;" alt="{\displaystyle {\sqrt {2}}}"></span> zenbaki irrazionala zela frogatu zuten. <a href="/wiki/Zenbaki_irrazional" title="Zenbaki irrazional">Zenbaki irrazional</a>en aurkikuntzak, matematikaren oinarrien historiako lehen krisia ekarri zuen, ordura arteko zenbait teoria zalantzan jartzen baitzituen; hala jaso zuen eskola pitagorikoko kide izan zen <a href="/w/index.php?title=Hippasus&action=edit&redlink=1" class="new" title="Hippasus (sortu gabe)">Hippasus</a> matematikariak. Ondorioz, batetik, zenbakien multzoan zenbaki osoen eta arrazionalen bereizketa definitu zen, eta bestetik <a href="/wiki/Luzera" class="mw-redirect" title="Luzera">luzera</a> edota <a href="/wiki/Proportzionaltasun_(matematika)" title="Proportzionaltasun (matematika)">proportzionaltasuna</a> bezalako kontzeptuak bereizi ziren (zenbaki arrazionaletan soilik erabiliko zirenak). Garapen horretan, <a href="/w/index.php?title=Zenbaki_poligonialak&action=edit&redlink=1" class="new" title="Zenbaki poligonialak (sortu gabe)">zenbaki poligonialak</a> eta beste zenbaki moten azterketa ere egin zuten. </p><p>Ezaguna da <a href="/wiki/Antzinako_Egipto" title="Antzinako Egipto">Antzinako Egipto</a>n eta <a href="/w/index.php?title=Vedetan&action=edit&redlink=1" class="new" title="Vedetan (sortu gabe)">Vedetan</a> jasotako materia aritmetikoetan aljebraren erabileraren zantzu batzuk ere lantzen direla. Era berean, <a href="/wiki/Hondarraren_teorema_txinatarra" class="mw-redirect" title="Hondarraren teorema txinatarra">hondarraren teorema txinatarra</a> ariketa gisa azaltzen da III eta V mendeetan idatzitako <a href="/w/index.php?title=Sunzi_Suanjing&action=edit&redlink=1" class="new" title="Sunzi Suanjing (sortu gabe)">Sunzi Suanjing</a> tratatu matematiko txinatarrean. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbakien_teoria_modernoa">Zenbakien teoria modernoa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=4" title="Aldatu atal hau: «Zenbakien teoria modernoa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=4" title="Edit section's source code: Zenbakien teoria modernoa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading4"><h4 id="Fermat">Fermat</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=5" title="Aldatu atal hau: «Fermat»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=5" title="Edit section's source code: Fermat"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <figure typeof="mw:File/Thumb"><a href="/wiki/Fitxategi:Pierre_de_Fermat.jpg" class="mw-file-description"><img src="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Pierre_de_Fermat.jpg/184px-Pierre_de_Fermat.jpg" decoding="async" width="184" height="246" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/f3/Pierre_de_Fermat.jpg/276px-Pierre_de_Fermat.jpg 1.5x, //upload.wikimedia.org/wikipedia/commons/f/f3/Pierre_de_Fermat.jpg 2x" data-file-width="299" data-file-height="400" /></a><figcaption><a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat (1607-1665)</a></figcaption></figure> <p><a href="/wiki/Pierre_de_Fermat" title="Pierre de Fermat">Pierre de Fermat</a> (1607-1665) frantziar abokatu eta matematikaria izan zen. Zenbakien teoriari buruz egin zuen lanaren zati handiena beste matematikari batzuei idatzitako gutunetan eta ohar pribatuetan gorde da.<sup id="cite_ref-#1_2-0" class="reference"><a href="#cite_note-#1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> Gutun eta ohar hauetan ez zuen ia frogarik idatzi. </p><p>Bere bizitzan zehar, Fermatek zenbaki-teorian hainbat ekarpen egin zituen. Horien artean hauek dira nabarmenenak: </p> <ul><li>1638an, edozein zenbaki beste lau zenbaki edo gutxiagoren karratu bezala idatz daitekeela aldarrikatu zuen, nahiz eta frogarik ez izan.<sup id="cite_ref-3" class="reference"><a href="#cite_note-3"><span class="cite-bracket">[</span>3<span class="cite-bracket">]</span></a></sup></li> <li><a href="/wiki/Fermaten_teorema_txikia" title="Fermaten teorema txikia">Fermaten teorema txikia</a> (1640): p zenbaki lehenak ez badu zenbaki osoa zatitzen, orduan: <span class="mwe-math-element"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" 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> </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/5b71e80b05f598bfd9ac9618c87a94323e41e688" class="mwe-math-fallback-image-display mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:19.504ex; height:3.176ex;" alt="{\displaystyle a^{p-1}\equiv 1{\pmod {p}}}"></span></li> <li><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> problemak zenbaki osoetan soluzio ez-tribialik ez zuela frogatu zuen.<sup id="cite_ref-4" class="reference"><a href="#cite_note-4"><span class="cite-bracket">[</span>4<span class="cite-bracket">]</span></a></sup></li> <li><a href="/w/index.php?title=%22Fermaten_azkeneko_teorema%22&action=edit&redlink=1" class="new" title=""Fermaten azkeneko teorema" (sortu gabe)">"Fermaten azkeneko teorema":</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 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> <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 \forall n\geq 3}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi mathvariant="normal">∀</mi> <mi>n</mi> <mo>≥</mo> <mn>3</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \forall n\geq 3}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/18ddb6bf26d504163434e5953a54edc773a112df" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:6.948ex; height:2.343ex;" alt="{\displaystyle \forall n\geq 3}"></span> problemak ez du soluzio ez-tribialik.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Euler">Euler</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=6" title="Aldatu atal hau: «Euler»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=6" title="Edit section's source code: Euler"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Lagun batek Fermaten lan batzuk erakutsi zizkionean interesatu zen lehen aldiz zenbakien teorian <a href="/wiki/Leonhard_Euler" title="Leonhard Euler">Leonhard Euler</a> (1707-1783). Eulerrek zenbakien teorian egin zituen ekarpenen artean honakoak dira nabarmenenak: </p> <ul><li>Fermaten teorema txikia frogatu zuen, modulu ez-lehenetara orokortuz. Fermaten beste lan askorekin ere gauza bera egin zuen.</li> <li>Zatiki jarraituen eta <a href="/wiki/Pell-en_ekuazioa" class="mw-redirect" title="Pell-en ekuazioa">Pell-en ekuazioa</a>ren arteko erlazioa idatzi zuen.<sup id="cite_ref-#1_2-1" class="reference"><a href="#cite_note-#1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup></li> <li>Zenbakien teoria analitikoan lehen urratsak eman zituen.</li></ul> <div class="mw-heading mw-heading4"><h4 id="Lagrange">Lagrange</h4><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=7" title="Aldatu atal hau: «Lagrange»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=7" title="Edit section's source code: Lagrange"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/wiki/Joseph-Louis_Lagrange" title="Joseph-Louis Lagrange">Joseph Louis Lagrange</a> (1736-1813) Fermatek eta Eulerrek eginiko lan batzuk osorik frogatzeko gai izan zen, esate baterako, <a href="/w/index.php?title=Lau_karratuen_teorema&action=edit&redlink=1" class="new" title="Lau karratuen teorema (sortu gabe)">lau karratuen teorema</a>. Forma koadratikoak bere osotasunean aztertu zituen; <a href="/wiki/Baliokidetasun-erlazio" title="Baliokidetasun-erlazio">baliokidetasun erlazioa</a> definitu zuen eta forma murriztuan adierazi zuen. </p><p><a href="/wiki/Adrien-Marie_Legendre" title="Adrien-Marie Legendre">Adrien-Marie Legendrek</a>  (1752–1833)  erreziprokotasun koadratikoaren legea ezarri zuen. <a href="/wiki/Zenbaki_lehenen_teorema" title="Zenbaki lehenen teorema">Zenbaki lehenen teorema</a>ren eta <a href="/w/index.php?title=Dirichlet-en_teorema&action=edit&redlink=1" class="new" title="Dirichlet-en teorema (sortu gabe)">segida aritmetikoen Dirichlet-en teorema</a>ren konjeturak ezarri zituen. <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 ax^{2}+by^{2}+cz^{2}=0}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>a</mi> <msup> <mi>x</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>b</mi> <msup> <mi>y</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>+</mo> <mi>c</mi> <msup> <mi>z</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>=</mo> <mn>0</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle ax^{2}+by^{2}+cz^{2}=0}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/6e7c75ed5d8d24057cd1160d2dfc659972e903af" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:19.919ex; height:3.009ex;" alt="{\displaystyle ax^{2}+by^{2}+cz^{2}=0}"></span> ekuazioa sakon aztertu zuen<sup id="cite_ref-#1_2-2" class="reference"><a href="#cite_note-#1-2"><span class="cite-bracket">[</span>2<span class="cite-bracket">]</span></a></sup> eta zuzenen gaineko forma koadratikoak ere aztertu zituen. Zahartzaroan, fermaten azkeneko teorema  n=5 kasurako frogatu zuen. </p><p><a href="/w/index.php?title=Disquisitiones_Arithmeticae&action=edit&redlink=1" class="new" title="Disquisitiones Arithmeticae (sortu gabe)"><i>Disquisitiones Arithmeticae</i></a>  liburuan, Carl Friedrich Gaussek (1777-1855) erreziprokotasun kuadratikoaren legea frogatu zuen, eta <a href="/w/index.php?title=Forma_kuadratikoen_teoria&action=edit&redlink=1" class="new" title="Forma kuadratikoen teoria (sortu gabe)">forma koadratikoen teoria</a> garatu zuen. Kongruentzien notazioa erabiltzen lehenengoa izan zen eta konputazioaren arloan ere murgildu zen, lehentasun testa (zenbaki lehenak aurkitzeko testa) esaterako. Liburu horren azken atalean, unitatearen erroaren eta zenbaki-teoriaren lotura ezarri zuen. </p> <div class="mw-heading mw-heading3"><h3 id="Izaeraren_eta_azpieremuen_sorrera">Izaeraren eta azpieremuen sorrera</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=8" title="Aldatu atal hau: «Izaeraren eta azpieremuen sorrera»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=8" title="Edit section's source code: Izaeraren eta azpieremuen sorrera"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Hemeretzigarren mendearen hasieran, honako garapenak gertatu ziren: </p> <ul><li>Zenbaki-teoria azterketa eremu gisa ikusteak indarra hartu zuen.</li> <li>Zenbaki-teoria modernorako matematikaren beharrezko garapenak eman ziren: <a href="/wiki/Zenbaki_konplexu" title="Zenbaki konplexu">analisi konplexua</a>, <a href="/wiki/Talde-teoria" title="Talde-teoria">talde-teoria</a>, <a href="/wiki/Galoisen_teoria" title="Galoisen teoria">Galoisen teoria</a> …</li> <li>Zenbaki-teoriaren banaketa zenbaki-teoria modernoko azpiatal nagusietan, hala nola zenbaki analitikoen teoria eta zenbaki aljebraikoen teoria.</li></ul> <div class="mw-heading mw-heading2"><h2 id="Azpiatal_nagusiak">Azpiatal nagusiak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=9" title="Aldatu atal hau: «Azpiatal nagusiak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=9" title="Edit section's source code: Azpiatal nagusiak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Tresna_elementalak">Tresna elementalak</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=10" title="Aldatu atal hau: «Tresna elementalak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=10" title="Edit section's source code: Tresna elementalak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Metodo_elementala&action=edit&redlink=1" class="new" title="Metodo elementala (sortu gabe)">Metodo bat elementala</a> dela esaten da, bertan analisi konplexua erabiltzen ez bada.<sup id="cite_ref-5" class="reference"><a href="#cite_note-5"><span class="cite-bracket">[</span>5<span class="cite-bracket">]</span></a></sup> Adibidez, hasiera batean, zenbaki lehenen teorema analisi konplexua erabiliz frogatu zen (1896. urtean), baina 1949. urtera arte ez zen froga elementalik aurkitu. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbakien_teoria_analitikoa">Zenbakien teoria analitikoa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=11" title="Aldatu atal hau: «Zenbakien teoria analitikoa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=11" title="Edit section's source code: Zenbakien teoria analitikoa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbakien teoria analitikoa zenbaki osoen problemak ebazteko <a href="/wiki/Analisi_matematiko" title="Analisi matematiko">analisi matematikoa</a> erabiltzen duen zenbakien teoriaren azpiatal bat da. Azpiatal honetan gehien erabiltzen diren metodoen artean <a href="/w/index.php?title=Dirichleten_serieak&action=edit&redlink=1" class="new" title="Dirichleten serieak (sortu gabe)">Dirichleten serieak</a> eta <a href="/w/index.php?title=Riemannen_zeta_funtzioa&action=edit&redlink=1" class="new" title="Riemannen zeta funtzioa (sortu gabe)">Riemannen zeta funtzioak</a> daude. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbakien_teoria_aljebraikoa">Zenbakien teoria aljebraikoa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=12" title="Aldatu atal hau: «Zenbakien teoria aljebraikoa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=12" title="Edit section's source code: Zenbakien teoria aljebraikoa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbaki konplexu bat <a href="/wiki/Zenbaki_aljebraiko" title="Zenbaki aljebraiko">algebraikoa</a> dela esaten da, koefiziente arrazionalak dituen polinomio baten erroa bada; adibidez, <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}+x+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>x</mi> <mo>+</mo> <mn>1</mn> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle x^{2}+x+1}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/78235883dfed13f5c0c7b6fb5aa82c002a1ac649" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:10.557ex; height:2.843ex;" alt="{\displaystyle x^{2}+x+1}"></span> zenbakiaren erro guztiak. <a href="/w/index.php?title=Eraztunen_teoriako&action=edit&redlink=1" class="new" title="Eraztunen teoriako (sortu gabe)">Eraztunen teoriako</a> <a href="/w/index.php?title=Zenbaki_ideal&action=edit&redlink=1" class="new" title="Zenbaki ideal (sortu gabe)">zenbaki idealen</a>, <a href="/w/index.php?title=Idealen_teoria&action=edit&redlink=1" class="new" title="Idealen teoria (sortu gabe)">idealen teoriaren</a> eta <a href="/wiki/Balorazio" class="mw-redirect" title="Balorazio">balorazio</a>-teoriaren garapenarekin batera etorri zen zenbaki-teoria algebraikoaren garapena. </p><p><br /> Orain arte ikusitako hiru azpiatalekin, zenbaki baten faktorizazioa bakarra dela frogatzen da. </p> <div class="mw-heading mw-heading3"><h3 id="Geometria_Diofantikoa">Geometria Diofantikoa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=13" title="Aldatu atal hau: «Geometria Diofantikoa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=13" title="Edit section's source code: Geometria Diofantikoa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p><a href="/w/index.php?title=Geometria_diofantikoa&action=edit&redlink=1" class="new" title="Geometria diofantikoa (sortu gabe)">Geometria diofantikoa</a>ren oinarrizko problema ekuazio diofantiko batek soluziorik duen ala ez jakitean datza, eta baiezko kasuan, zenbat dituen jakitean. </p><p>Adibidez, bi aldagai errealen menpe  definitutako ekuazio batek kurba bat definitzen du planoan. Ideia orokortuz, bi aldagai edo gehiagoren menpe definitutako ekuazio batek edo ekuazio-sistema batek <a href="/wiki/Kurba_(matematika)" title="Kurba (matematika)">kurba</a> bat, <a href="/wiki/Gainazal" title="Gainazal">gainazal</a> bat edo n dimentsioko espazioko objektu bat definitzen du. Geometria diofantikoan, problemak ea balio arrazionaletarako edo osotarako soluziorik duen aztertzen da. Baiezko kasuan, zenbat dauden eta lantzen ari garen espazioan nola banatuta dauden jakitea da hurrengo urratsa. Horretarako, soluzio kopurua ea finitua den eta bere kontagarritasuna aztertu behar da. </p> <div class="mw-heading mw-heading2"><h2 id="Beste_eremu_batzuk">Beste eremu batzuk</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=14" title="Aldatu atal hau: «Beste eremu batzuk»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=14" title="Edit section's source code: Beste eremu batzuk"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <div class="mw-heading mw-heading3"><h3 id="Konbinatoria_aritmetikoa">Konbinatoria aritmetikoa</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=15" title="Aldatu atal hau: «Konbinatoria aritmetikoa»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=15" title="Edit section's source code: Konbinatoria aritmetikoa"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Konbinatoria aritmetikoak honako galdera hauek hartzen ditu abiapuntutzat: A multzo “txiki” eta infinitu bat hartzen badugu, multzo honek<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,a+b,a+2b,....,a+10b\}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mo fence="false" stretchy="false">{</mo> <mi>a</mi> <mo>,</mo> <mi>a</mi> <mo>+</mo> <mi>b</mi> <mo>,</mo> <mi>a</mi> <mo>+</mo> <mn>2</mn> <mi>b</mi> <mo>,</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>.</mo> <mo>,</mo> <mi>a</mi> <mo>+</mo> <mn>10</mn> <mi>b</mi> <mo fence="false" stretchy="false">}</mo> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle \{a,a+b,a+2b,....,a+10b\}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c462e921e3d6e0cfefbec56ebac198b7b6aa81b2" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:30.517ex; height:2.843ex;" alt="{\displaystyle \{a,a+b,a+2b,....,a+10b\}}"></span> <a href="/wiki/Progresio_aritmetiko" title="Progresio aritmetiko">segida aritmetiko</a>ko zenbat elementu izango ditu? Posible izango al da multzoko elementuen batura bidez, balio batetik gorako elementuak idaztea? Multzoko elementuen batura ekuazio modura hartuta lortzen diren ekuazioei <a href="/wiki/Konbinatoria" title="Konbinatoria">konbinatoria</a> aritmetikoko karakteristikak deritze. </p><p>Eremu hau, aipatutako ekuazioen azterketan oinarritzen denez, zenbaki-teoria batukorra eta zenbakien <a href="/wiki/Geometria" title="Geometria">geometria</a> erabiltzen dira. Orokorrean, azaltzen diren problemak <a href="/wiki/Talde-teoria" title="Talde-teoria">talde-teoria</a> finituarekin, <a href="/w/index.php?title=Modelo_teoria&action=edit&redlink=1" class="new" title="Modelo teoria (sortu gabe)">modelo teoria</a>rekin eta <a href="/w/index.php?title=Teoria_ergodikoa&action=edit&redlink=1" class="new" title="Teoria ergodikoa (sortu gabe)">teoria ergodikoa</a>rekin erlazionatuta daude. </p> <div class="mw-heading mw-heading3"><h3 id="Zenbaki-teoria_konputazionala">Zenbaki-teoria konputazionala</h3><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=16" title="Aldatu atal hau: «Zenbaki-teoria konputazionala»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=16" title="Edit section's source code: Zenbaki-teoria konputazionala"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Soluzioak lortzeko metodoen deskribapena frogapenak egitearen ideia baino lehenagotik dator. Metodo hauek (<a href="/wiki/Algoritmo" title="Algoritmo">algoritmoak</a>) lehen aldiz historian <a href="/wiki/Antzinako_Grezia" title="Antzinako Grezia">antzinako Grezian</a> azaltzen dira. Horren adibidea da <a href="/wiki/Euklidesen_algoritmo" title="Euklidesen algoritmo">algoritmo euklidearra</a>: zenbaki-teorian algoritmo euklidearra erabiltzen den modua, konputazioan algoritmo euklidearra erabiltzen den modua baino zaharragoa da. </p><p>Orokorrean, bi arazo izango ditugu, edo izango al ditugun jakin nahiko dugu.  Batetik, ea konputatzeko gai izango garen, eta beraz, ea konputazionalki emaitza bat lortuko dugun. Bestetik, ea zenbat iraungo duen kalkulu konputazionalak, hau da, kostu konputazionala zenbatekoa izango den. Agian, erraza izan daiteke zenbaki bat lehena den erabakitzea, baina konputazionalki modu eraginkor eta azkarrean egitea oso zaila izan daiteke (zenbakia oso handia bada, baliteke kalkulu gehiegi egin behar izatea). Gaur egun, badira <a href="/wiki/Zenbaki_lehenen_test" title="Zenbaki lehenen test">lehentasun test</a> azkarrak, baina <a href="/wiki/Faktorizazio" title="Faktorizazio">faktorizaziorako</a> test azkarrak falta dira. </p><p>Kriptografian, mezu bat, bere hartzailearentzat (eta soilik berarentzat) ulergarria izatea lortu nahi da, horretarako pribatutasuna bermatuz. Hari beretik, demagun zifratutako mezu bat dugula, kodifikatuta. Deskodeketa egiteko, zifratutako mezua zenbakitzat hartuz, hau faktore lehenetan deskonposatzea premiazkoa da ia beti (gaur egun erabiltzen diren sistema kriptografikoetan), eta hau konputazionalki programatzeko, lehentasun test azkarren beharra dugu. Mezu baten pribatutasuna bermatzeko (baina gero mezua deskodetu ahal izateko), zenbaki lehenetan deskonposatzeko oso konplexuak diren zenbakiak erabiltzen dira. Horrela, mezuaren hartzailea ez den batek faktorizatzeko test azkarrik ez dagoenez, ezingo du deskodetu, eta beraz, pribatutasuna mantentzen da. </p> <div class="mw-heading mw-heading2"><h2 id="Aplikazioak">Aplikazioak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=17" title="Aldatu atal hau: «Aplikazioak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=17" title="Edit section's source code: Aplikazioak"><span>aldatu iturburu kodea</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Zenbaki teoria elementala matematika diskretuko kurtsoetan irakasten da zientzia konputazionalerako. Horrez gain, zenbaki teoriak aplikazio ugari ditu analisi numerikoan, bai eta aski ezaguna den <a href="/wiki/Kriptografia" title="Kriptografia">kriptografia</a>n ere.<sup id="cite_ref-6" class="reference"><a href="#cite_note-6"><span class="cite-bracket">[</span>6<span class="cite-bracket">]</span></a></sup> <sup id="cite_ref-7" class="reference"><a href="#cite_note-7"><span class="cite-bracket">[</span>7<span class="cite-bracket">]</span></a></sup> </p> <div class="mw-heading mw-heading2"><h2 id="Erreferentziak">Erreferentziak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=18" title="Aldatu atal hau: «Erreferentziak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=Zenbakien_teoria&action=edit&section=18" title="Edit section's source code: Erreferentziak"><span>aldatu iturburu kodea</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"><a href="#cite_ref-1">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFColilli1981-01">Colilli, Paul.  (1981-01). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.3138/cmlr.37.2.351">«Bernardo, Aldo S. and Rigo Mignani. Ritratto Dell’Italia. 2nd Ed. Lexington, Massachusetts and Toronto: D.C. Heath and Company, 1978Bernardo, Aldo S. and Rigo Mignani. Ritratto Dell’Italia. 2nd Ed. Lexington, Massachusetts and Toronto: D.C. Heath and Company, 1978. Pp. IX, 317.»</a> <i>Canadian Modern Language Review</i> 37 (2): 351–352.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.3138%2Fcmlr.37.2.351">10.3138/cmlr.37.2.351</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/0008-4506">0008-4506</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-12)</small></span></span>.</span> </li> <li id="cite_note-#1-2">↑ <a href="#cite_ref-#1_2-0"><sup><b>a</b></sup></a> <a href="#cite_ref-#1_2-1"><sup><b>b</b></sup></a> <a href="#cite_ref-#1_2-2"><sup><b>c</b></sup></a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFWeil,_André,_1906-1998.1984">Weil, André, 1906-1998..  (1984). <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/9576587"><i>Number theory : an approach through history from Hammurapi to Legendre. </i></a> Birkhäuser <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/0-8176-3141-0" title="Berezi:BookSources/0-8176-3141-0">0-8176-3141-0</a>. <a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a> <a rel="nofollow" class="external text" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=9576587">9576587</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-12)</small></span></span>.</span> </li> <li id="cite_note-3"><a href="#cite_ref-3">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation"> <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/1013584750"><i>Numbers and measurements. </i></a> (First edition. argitaraldia) <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/978-1-5383-0042-8" title="Berezi:BookSources/978-1-5383-0042-8">978-1-5383-0042-8</a>. <a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a> <a rel="nofollow" class="external text" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1013584750">1013584750</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-12)</small></span></span>.</span> </li> <li id="cite_note-4"><a href="#cite_ref-4">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFFermatApolloniusBillyHenry1891">Fermat, Pierre de; Apollonius; Billy, Jacques de; Henry, Charles; Tannery, Paul; Tannery, Paul; Wallis, John.  (1891). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.5962/bhl.title.22243"><i>Oeuvres de Fermat / publiées par les soins de MM. Paul Tannery et Charles Henry sous les auspices du Ministère de l'instruction publique.. </i></a> Gauthier-Villars et fils, <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-12)</small></span></span>.</span> </li> <li id="cite_note-5"><a href="#cite_ref-5">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFApostol,_Tom_M.,">Apostol, Tom M.,. <a rel="nofollow" class="external text" href="https://www.worldcat.org/oclc/1859863"><i>Introduction to analytic number theory. </i></a> <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/0-387-90163-9" title="Berezi:BookSources/0-387-90163-9">0-387-90163-9</a>. <a href="/wiki/PubMed_Central" class="mw-redirect" title="PubMed Central">PMC</a> <a rel="nofollow" class="external text" href="http://www.pubmedcentral.nih.gov/articlerender.fcgi?tool=pmcentrez&artid=1859863">1859863</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-12)</small></span></span>.</span> </li> <li id="cite_note-6"><a href="#cite_ref-6">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation" id="CITEREFGUNNELLSYASAKI2012-11-13">GUNNELLS, PAUL E.; YASAKI, DAN.  (2012-11-13). <a rel="nofollow" class="external text" href="https://dx.doi.org/10.1142/s1793042112501242">«MODULAR FORMS AND ELLIPTIC CURVES OVER THE CUBIC FIELD OF DISCRIMINANT –23»</a> <i>International Journal of Number Theory</i> 09 (01): 53–76.  <a href="/wiki/Digital_object_identifier" title="Digital object identifier">doi</a>:<span class="neverexpand"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1142%2Fs1793042112501242">10.1142/s1793042112501242</a></span>. <a href="/wiki/International_Standard_Serial_Number" class="mw-redirect" title="International Standard Serial Number">ISSN</a> <a rel="nofollow" class="external text" href="http://worldcat.org/issn/1793-0421">1793-0421</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-12)</small></span></span>.</span> </li> <li id="cite_note-7"><a href="#cite_ref-7">↑</a> <span class="reference-text"><span class="citation"></span> <span class="citation"><a rel="nofollow" class="external text" href="https://dx.doi.org/10.1090/chel/375/06">«Applications of formal groups in algebraic topology, number theory, and algebraic geometry»</a> <i>Formal Groups and Applications</i> (American Mathematical Society): 427–477. 2012-12-07 <a href="/wiki/International_Standard_Book_Number" title="International Standard Book Number">ISBN</a> <a href="/wiki/Berezi:BookSources/978-0-8218-5349-8" title="Berezi:BookSources/978-0-8218-5349-8">978-0-8218-5349-8</a>. <span class="reference-accessdate"><small>(Noiz kontsultatua: 2020-11-12)</small></span></span>.</span> </li> </ol></div> <div class="mw-heading mw-heading2"><h2 id="Kanpo_estekak">Kanpo estekak</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=Zenbakien_teoria&veaction=edit&section=19" title="Aldatu atal hau: «Kanpo estekak»" class="mw-editsection-visualeditor"><span>aldatu</span></a><span class="mw-editsection-divider"> | </span><a 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.navbox-title{background-color:#ddf}.mw-parser-output .navbox-subgroup .navbox-group,.mw-parser-output .navbox-subgroup .navbox-abovebelow{background-color:#e6e6ff}.mw-parser-output .navbox-even{background-color:#f7f7f7}.mw-parser-output .navbox-odd{background-color:transparent}.mw-parser-output .navbox .hlist td dl,.mw-parser-output .navbox .hlist td ol,.mw-parser-output .navbox .hlist td ul,.mw-parser-output .navbox td.hlist 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}</style></div><div role="navigation" class="navbox" aria-labelledby="Autoritate_kontrola" style="width: inherit;padding:3px"><table class="nowraplinks hlist navbox-inner" style="border-spacing:0;background:transparent;color:inherit"><tbody><tr><th id="Autoritate_kontrola" scope="row" class="navbox-group" style="width:1%;width: 12%; text-align:center;"><a href="/wiki/Laguntza:Autoritate_kontrola" title="Laguntza:Autoritate kontrola">Autoritate kontrola</a></th><td class="navbox-list-with-group navbox-list navbox-odd" style="width:100%;padding:0"><div style="padding:0 0.25em"> <ul><li><b>Wikimedia proiektuak</b></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q12479" class="extiw" title="wikidata:Q12479">Q12479</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Number_theory">Number theory</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q12479%22">Q12479</a></span></span></li></ul> <hr /> <ul><li><b>Identifikadoreak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioteca_Nacional_de_Espa%C3%B1a" class="mw-redirect" title="Biblioteca Nacional de España">BNE</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://datos.bne.es/resource/XX4703223">XX4703223</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Biblioth%C3%A8que_nationale_de_France" class="mw-redirect" title="Bibliothèque nationale de France">BNF</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://catalogue.bnf.fr/ark:/12148/cb131627085">131627085</a> <a rel="nofollow" class="external text" href="http://data.bnf.fr/ark:/12148/cb131627085">(data)</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Integrated_Authority_File" class="mw-redirect" title="Integrated Authority File">GND</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://d-nb.info/gnd/4067277-3">4067277-3</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Library_of_Congress_Control_Number" title="Library of Congress Control Number">LCCN</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.loc.gov/authorities/sh85093222">sh85093222</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/National_Diet_Library" class="mw-redirect" title="National Diet Library">NDL</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://id.ndl.go.jp/auth/ndlna/00570429">00570429</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/National_Library_of_the_Czech_Republic" class="mw-redirect" title="National Library of the Czech Republic">NKC</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://aleph.nkp.cz/F/?func=find-c&local_base=aut&ccl_term=ica=ph126576">ph126576</a></span></li> <li><span style="white-space:nowrap;"><a href="/wiki/Syst%C3%A8me_universitaire_de_documentation" title="Système universitaire de documentation">SUDOC</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://www.idref.fr/027270475">027270475</a></span></li> <li><b>Hiztegiak eta entziklopediak</b></li> <li><span style="white-space:nowrap;"><a href="/wiki/Encyclop%C3%A6dia_Britannica" title="Encyclopædia Britannica">Britannica</a>:</span> <span class="uid"><a rel="nofollow" class="external text" href="https://www.britannica.com/topic/number-theory">url</a></span></li></ul> </div></td></tr></tbody></table></div><div class="mw-mf-linked-projects hlist"> <ul><li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikidata" title="Wikidata"><img alt="Wd" src="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/20px-Wikidata-logo.svg.png" decoding="async" width="20" height="11" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/30px-Wikidata-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/f/ff/Wikidata-logo.svg/40px-Wikidata-logo.svg.png 2x" data-file-width="1050" data-file-height="590" /></a></span> Datuak:</span> <span class="uid"><a href="https://www.wikidata.org/wiki/Q12479" class="extiw" title="wikidata:Q12479">Q12479</a></span></li> <li><span style="white-space:nowrap;"><span typeof="mw:File"><a href="/wiki/Wikimedia_Commons" title="Commonscat"><img alt="Commonscat" src="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/15px-Commons-logo.svg.png" decoding="async" width="15" height="20" class="mw-file-element" srcset="//upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/23px-Commons-logo.svg.png 1.5x, //upload.wikimedia.org/wikipedia/commons/thumb/4/4a/Commons-logo.svg/30px-Commons-logo.svg.png 2x" data-file-width="1024" data-file-height="1376" /></a></span> Multimedia:</span> <span class="uid"><span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Category:Number_theory">Number theory</a></span> / <span class="plainlinks"><a class="external text" href="https://commons.wikimedia.org/wiki/Special:MediaSearch?type=image&search=%22Q12479%22">Q12479</a></span></span></li></ul> </div></div>    </div><script>(RLQ=window.RLQ||[]).push(function(){mw.log.warn("Gadget \"ErrefAurrebista\" was not loaded. 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