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title="អ្នកត្រូវបានលើកទឹកចិត្តបង្កើតគណនីនិងកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។" class=""><span>បង្កើតគណនី</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=%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%80%E1%9E%8F%E1%9F%8B%E1%9E%88%E1%9F%92%E1%9E%98%E1%9F%84%E1%9F%87%E1%9E%85%E1%9E%BC%E1%9E%9B%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%A2%E1%9F%92%E1%9E%93%E1%9E%80%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%BE%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%B6%E1%9E%9F%E1%9F%8B&returnto=%E1%9E%85%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%93%E1%9E%A2%E1%9E%BC%E1%9E%8F%E1%9E%BC%E1%9E%98%E1%9F%89%E1%9E%A0%E1%9F%92%E1%9E%9C%E1%9E%B8%E1%9E%9F" title="អ្នកត្រូវបានលើកទឹកចិត្តឱ្យកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។ [o]" accesskey="o" class=""><span>កត់ឈ្មោះចូល</span></a> </li> </ul> </div> </div> </div> <div id="vector-user-links-dropdown" class="vector-dropdown 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id="pt-sitesupport" class="user-links-collapsible-item mw-list-item"><a href="https://donate.wikimedia.org/?wmf_source=donate&wmf_medium=sidebar&wmf_campaign=km.wikipedia.org&uselang=km"><span>បរិច្ចាគ</span></a></li><li id="pt-createaccount" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%94%E1%9E%84%E1%9F%92%E1%9E%80%E1%9E%BE%E1%9E%8F%E1%9E%82%E1%9E%8E%E1%9E%93%E1%9E%B8&returnto=%E1%9E%85%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%93%E1%9E%A2%E1%9E%BC%E1%9E%8F%E1%9E%BC%E1%9E%98%E1%9F%89%E1%9E%A0%E1%9F%92%E1%9E%9C%E1%9E%B8%E1%9E%9F" title="អ្នកត្រូវបានលើកទឹកចិត្តបង្កើតគណនីនិងកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។"><span class="vector-icon mw-ui-icon-userAdd mw-ui-icon-wikimedia-userAdd"></span> <span>បង្កើតគណនី</span></a></li><li id="pt-login" class="user-links-collapsible-item mw-list-item"><a href="/w/index.php?title=%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%80%E1%9E%8F%E1%9F%8B%E1%9E%88%E1%9F%92%E1%9E%98%E1%9F%84%E1%9F%87%E1%9E%85%E1%9E%BC%E1%9E%9B%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%A2%E1%9F%92%E1%9E%93%E1%9E%80%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%BE%E1%9E%94%E1%9F%92%E1%9E%9A%E1%9E%B6%E1%9E%9F%E1%9F%8B&returnto=%E1%9E%85%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%93%E1%9E%A2%E1%9E%BC%E1%9E%8F%E1%9E%BC%E1%9E%98%E1%9F%89%E1%9E%A0%E1%9F%92%E1%9E%9C%E1%9E%B8%E1%9E%9F" title="អ្នកត្រូវបានលើកទឹកចិត្តឱ្យកត់ឈ្មោះចូល។ ប៉ុន្តែនេះមិនមែនជាការបង្ខំទេ។ [o]" accesskey="o"><span class="vector-icon mw-ui-icon-logIn mw-ui-icon-wikimedia-logIn"></span> <span>កត់ឈ្មោះចូល</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"> ទំព័រសម្រាប់អ្នកកែសម្រួលដែលបានកត់ឈ្មោះចេញ <a href="/wiki/%E1%9E%87%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%99:Introduction" aria-label="ស្វែងយល់បន្ថែមអំពីការកែសម្រួល"><span>ស្វែងយល់បន្ថែម</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/%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%9A%E1%9E%BD%E1%9E%98%E1%9E%85%E1%9F%86%E1%9E%8E%E1%9F%82%E1%9E%80%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%81%E1%9F%92%E1%9E%89%E1%9E%BB%E1%9F%86" title="បញ្ជីកំណែប្រែធ្វើឡើងពីអាសយដ្ឋាន IP នេះ [y]" accesskey="y"><span>ការរួមចំណែក</span></a></li><li id="pt-anontalk" class="mw-list-item"><a href="/wiki/%E1%9E%96%E1%9E%B7%E1%9E%9F%E1%9F%81%E1%9E%9F:%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9E%96%E1%9E%B7%E1%9E%97%E1%9E%B6%E1%9E%80%E1%9F%92%E1%9E%9F%E1%9E%B6%E1%9E%9A%E1%9E%94%E1%9E%9F%E1%9F%8B%E1%9E%81%E1%9F%92%E1%9E%89%E1%9E%BB%E1%9F%86" title="ការពិភាក្សាអំពីកំណែប្រែដែលធ្វើឡើងចេញពីអាសយដ្ឋាន IP នេះ [n]" accesskey="n"><span>ការពិភាក្សា</span></a></li> </ul> </div> </div> </div> </div> </nav> </div> </header> 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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">មាតិកា</h2> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-toc.pin">ប្ដូរទីតាំងទៅរបារចំហៀង</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-toc.unpin">លាក់</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">ក្បាលទំព័រ</div> </a> </li> <li id="toc-តារាងនៃចំនួនអូតូម៉ហ្វីស" class="vector-toc-list-item vector-toc-level-1 vector-toc-list-item-expanded"> <a class="vector-toc-link" href="#តារាងនៃចំនួនអូតូម៉ហ្វីស"> <div class="vector-toc-text"> <span class="vector-toc-numb">១</span> <span>តារាងនៃចំនួនអូតូម៉ហ្វីស</span> </div> </a> <ul id="toc-តារាងនៃចំនួនអូតូម៉ហ្វីស-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="មាតិកា" 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="Toggle the table of contents" > <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">Toggle the table of contents</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">ចំនួនអូតូម៉ហ្វីស</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="Go to an article in another language. Available in ១៤ languages" > <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-14" 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">១៤ ភាសា</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-en mw-list-item"><a href="https://en.wikipedia.org/wiki/Automorphic_number" title="Automorphic number – អង់គ្លេស" lang="en" hreflang="en" data-title="Automorphic number" data-language-autonym="English" data-language-local-name="អង់គ្លេស" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-fi mw-list-item"><a href="https://fi.wikipedia.org/wiki/Automorfinen_luku" title="Automorfinen luku – ហ្វាំងឡង់" lang="fi" hreflang="fi" data-title="Automorfinen luku" data-language-autonym="Suomi" data-language-local-name="ហ្វាំងឡង់" class="interlanguage-link-target"><span>Suomi</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/Nombre_automorphe" title="Nombre automorphe – បារាំង" lang="fr" hreflang="fr" data-title="Nombre automorphe" data-language-autonym="Français" data-language-local-name="បារាំង" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-he mw-list-item"><a href="https://he.wikipedia.org/wiki/%D7%9E%D7%A1%D7%A4%D7%A8_%D7%90%D7%95%D7%98%D7%95%D7%9E%D7%95%D7%A8%D7%A4%D7%99" title="מספר אוטומורפי – ហេប្រឺ" lang="he" hreflang="he" data-title="מספר אוטומורפי" data-language-autonym="עברית" data-language-local-name="ហេប្រឺ" class="interlanguage-link-target"><span>עברית</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/Automorfikus_sz%C3%A1mok" title="Automorfikus számok – ហុងគ្រី" lang="hu" hreflang="hu" data-title="Automorfikus számok" data-language-autonym="Magyar" data-language-local-name="ហុងគ្រី" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/Numero_automorfo" title="Numero automorfo – អ៊ីតាលី" lang="it" hreflang="it" data-title="Numero automorfo" data-language-autonym="Italiano" data-language-local-name="អ៊ីតាលី" 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/%E8%87%AA%E5%B7%B1%E5%90%8C%E5%BD%A2%E6%95%B0" title="自己同形数 – ជប៉ុន" lang="ja" hreflang="ja" data-title="自己同形数" data-language-autonym="日本語" data-language-local-name="ជប៉ុន" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-lt mw-list-item"><a href="https://lt.wikipedia.org/wiki/Automorfinis_skai%C4%8Dius" title="Automorfinis skaičius – លីទុយអានី" lang="lt" hreflang="lt" data-title="Automorfinis skaičius" data-language-autonym="Lietuvių" data-language-local-name="លីទុយអានី" class="interlanguage-link-target"><span>Lietuvių</span></a></li><li class="interlanguage-link interwiki-nl mw-list-item"><a href="https://nl.wikipedia.org/wiki/Automorf_getal" title="Automorf getal – ហូឡង់" lang="nl" hreflang="nl" data-title="Automorf getal" data-language-autonym="Nederlands" data-language-local-name="ហូឡង់" class="interlanguage-link-target"><span>Nederlands</span></a></li><li class="interlanguage-link interwiki-pl mw-list-item"><a href="https://pl.wikipedia.org/wiki/Liczby_automorficzne" title="Liczby automorficzne – ប៉ូឡូញ" lang="pl" hreflang="pl" data-title="Liczby automorficzne" data-language-autonym="Polski" data-language-local-name="ប៉ូឡូញ" class="interlanguage-link-target"><span>Polski</span></a></li><li class="interlanguage-link interwiki-ro mw-list-item"><a href="https://ro.wikipedia.org/wiki/Num%C4%83r_automorf" title="Număr automorf – រូម៉ានី" lang="ro" hreflang="ro" data-title="Număr automorf" data-language-autonym="Română" data-language-local-name="រូម៉ានី" 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%90%D0%B2%D1%82%D0%BE%D0%BC%D0%BE%D1%80%D1%84%D0%BD%D0%BE%D0%B5_%D1%87%D0%B8%D1%81%D0%BB%D0%BE" title="Автоморфное число – រុស្ស៊ី" lang="ru" hreflang="ru" data-title="Автоморфное число" data-language-autonym="Русский" data-language-local-name="រុស្ស៊ី" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sl mw-list-item"><a href="https://sl.wikipedia.org/wiki/Avtomorfno_%C5%A1tevilo" title="Avtomorfno število – ស្លូវ៉ានី" lang="sl" hreflang="sl" data-title="Avtomorfno število" data-language-autonym="Slovenščina" data-language-local-name="ស្លូវ៉ានី" class="interlanguage-link-target"><span>Slovenščina</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/%E8%87%AA%E5%AE%88%E6%95%B0" title="自守数 – ចិន" lang="zh" hreflang="zh" data-title="自守数" data-language-autonym="中文" data-language-local-name="ចិន" class="interlanguage-link-target"><span>中文</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/Q2313686#sitelinks-wikipedia" title="កែប្រែតំណភ្ជាប់អន្តរភាសា" class="wbc-editpage">កែប្រែតំណភ្ជាប់</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="លំហឈ្មោះ"> <div 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class="vector-page-tools-landmark" aria-label="Page tools"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Appearance"> <div id="vector-appearance-pinned-container" class="vector-pinned-container"> <div id="vector-appearance" class="vector-appearance vector-pinnable-element"> <div class="vector-pinnable-header vector-appearance-pinnable-header vector-pinnable-header-pinned" data-feature-name="appearance-pinned" data-pinnable-element-id="vector-appearance" data-pinned-container-id="vector-appearance-pinned-container" data-unpinned-container-id="vector-appearance-unpinned-container" > <div class="vector-pinnable-header-label">Appearance</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">ប្ដូរទីតាំងទៅរបារចំហៀង</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">លាក់</button> </div> </div> </div> </nav> </div> </div> <div id="bodyContent" class="vector-body" aria-labelledby="firstHeading" data-mw-ve-target-container> <div class="vector-body-before-content"> <div class="mw-indicators"> </div> <div id="siteSub" class="noprint">ពីវិគីភីឌា</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="km" dir="ltr"><p>ក្នុង<a href="/wiki/%E1%9E%82%E1%9E%8E%E1%9E%B7%E1%9E%8F%E1%9E%9C%E1%9E%B7%E1%9E%91%E1%9F%92%E1%9E%99%E1%9E%B6" title="គណិតវិទ្យា">គណិតវិទ្យា</a> <b>ចំនួនអូតូម៉ហ្វីស</b>(Automorphic number) គឺជាចំនួនដែលខ្ទង់ចុងក្រោយនៃ<a href="/w/index.php?title=%E1%9E%80%E1%9E%B6%E1%9E%9A%E1%9F%81&action=edit&redlink=1" class="new" title="ការេ (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">ការេ</a>របស់វាដូចនឹងខ្ទង់ចុងក្រោយនៃលេខដើម ។ ឧទាហរណ៍ 5<sup>2</sup> = 2<i>5</i>, 76<sup>2</sup> = 57<i>76</i> និង 890625<sup>2</sup> = 793212<i>890625</i> ។ </p><p>ចំនួនអូតូម៉ហ្វីសផ្តើមដោយលេខ <a href="/w/index.php?title=%E1%9F%A1%E2%80%8B&action=edit&redlink=1" class="new" title="១ (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">១</a> , <a href="/wiki/%E1%9F%A5" title="៥">៥</a> , ៦ , ២៥ , ៧៦ , ៣៧៦ , ៦២៥ , ៩៣៧៦.... ។ </p><p>អោយ ចំនួនអូតូម៉ហ្វីស<span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n>1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>></mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n>1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/0f75691c789e88981a5e1e5b805f2e6f331ec932" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:6.043ex; height:2.176ex;" alt="{\displaystyle n>1\,}"></span> ដែលមាន <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 k\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5665cb00a844c1c6a671c119c6e4984d28fb851" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.598ex; height:2.176ex;" alt="{\displaystyle k\,}"></span>ខ្ទង់ ចំនួនអូតូម៉ហ្វីស <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n'\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mo>′</mo> </msup> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n'\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/25a94565b0c3e69c749dd5ed45cd61f18e8b0d72" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:2.467ex; height:2.509ex;" alt="{\displaystyle n'\,}"></span>ដែលមាន2kខ្ទង់អាចត្រូវគេសំដែងដោយរូបមន្ត <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n'=3\cdot n^{2}-2\cdot n^{3}{\bmod {10^{2k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>n</mi> <mo>′</mo> </msup> <mo>=</mo> <mn>3</mn> <mo>⋅</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> <mo>−</mo> <mn>2</mn> <mo>⋅</mo> <msup> <mi>n</mi> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> <mrow class="MJX-TeXAtom-ORD"> <mo lspace="thickmathspace" rspace="thickmathspace">mod</mo> <mrow class="MJX-TeXAtom-ORD"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> <mi>k</mi> </mrow> </msup> </mrow> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n'=3\cdot n^{2}-2\cdot n^{3}{\bmod {10^{2k}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/71bbdf645ab2f769e3bacdde7c0897611e379758" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:28.516ex; height:2.843ex;" alt="{\displaystyle n'=3\cdot n^{2}-2\cdot n^{3}{\bmod {10^{2k}}}}"></span> ។ </p><p>យ៉ាងហោចណាស់ មានចំនួនចំនួនអូតូម៉ហ្វីសដែលមាន<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 k\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>k</mi> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle k\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a5665cb00a844c1c6a671c119c6e4984d28fb851" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.598ex; height:2.176ex;" alt="{\displaystyle k\,}"></span>ខ្ទង់ មួយបញ្ចប់ដោយ ៥ និងមួយផ្សេងទៀតបញ្ចប់ដោយ ៦ ។ មួយក្នុងចំនោមនោះមានទំរង់ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\equiv 0{\pmod {2^{k}}},n\equiv 1{\pmod {5^{k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≡</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mi>n</mi> <mo>≡</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <msup> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\equiv 0{\pmod {2^{k}}},n\equiv 1{\pmod {5^{k}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/274e94cb6083eedae523ed00480cabff3a119f79" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.216ex; height:3.176ex;" alt="{\displaystyle n\equiv 0{\pmod {2^{k}}},n\equiv 1{\pmod {5^{k}}}}"></span> ហើងផ្សេងទៀតមានទំរង់ <span class="mwe-math-element"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle n\equiv 1{\pmod {2^{k}}},n\equiv 0{\pmod {5^{k}}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mi>n</mi> <mo>≡</mo> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> <mo>,</mo> <mi>n</mi> <mo>≡</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mspace width="1em" /> <mo stretchy="false">(</mo> <mi>mod</mi> <mspace width="0.333em" /> <msup> <mn>5</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo stretchy="false">)</mo> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle n\equiv 1{\pmod {2^{k}}},n\equiv 0{\pmod {5^{k}}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/bb279184fb6564ce8b392a4e71c3b998c10b6f15" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:36.216ex; height:3.176ex;" alt="{\displaystyle n\equiv 1{\pmod {2^{k}}},n\equiv 0{\pmod {5^{k}}}}"></span> ។ ផលបូកនៃពីរចំនួននោះគឺ <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 10^{k}+1\,}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mn>10</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> <mo>+</mo> <mn>1</mn> <mspace width="thinmathspace" /> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 10^{k}+1\,}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/c7809fb0b88c4d05d841e82dfa16fec725246a2b" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.505ex; width:7.804ex; height:2.843ex;" alt="{\displaystyle 10^{k}+1\,}"></span> ។ </p> <div class="mw-heading mw-heading2"><h2 id="តារាងនៃចំនួនអូតូម៉ហ្វីស"><span id=".E1.9E.8F.E1.9E.B6.E1.9E.9A.E1.9E.B6.E1.9E.84.E1.9E.93.E1.9F.83.E1.9E.85.E1.9F.86.E1.9E.93.E1.9E.BD.E1.9E.93.E1.9E.A2.E1.9E.BC.E1.9E.8F.E1.9E.BC.E1.9E.98.E1.9F.89.E1.9E.A0.E1.9F.92.E1.9E.9C.E1.9E.B8.E1.9E.9F"></span>តារាងនៃចំនួនអូតូម៉ហ្វីស</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=%E1%9E%85%E1%9F%86%E1%9E%93%E1%9E%BD%E1%9E%93%E1%9E%A2%E1%9E%BC%E1%9E%8F%E1%9E%BC%E1%9E%98%E1%9F%89%E1%9E%A0%E1%9F%92%E1%9E%9C%E1%9E%B8%E1%9E%9F&action=edit&section=1" title="កែប្រែផ្នែក៖ តារាងនៃចំនួនអូតូម៉ហ្វីស"><span>កែប្រែ</span></a><span class="mw-editsection-bracket">]</span></span></div> <table border="2"> <tbody><tr bgcolor="#90ee90"> <th><i>n</i> </th> <th><i>n</i><sup>2</sup> </th></tr> <tr> <td align="right"><a href="/w/index.php?title=5_(nombre)&action=edit&redlink=1" class="new" title="5 (nombre) (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">5</a> </td> <td align="right"><a href="/w/index.php?title=25_(nombre)&action=edit&redlink=1" class="new" title="25 (nombre) (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">2<b>5</b></a> </td></tr> <tr> <td align="right"><a href="/w/index.php?title=25_(nombre)&action=edit&redlink=1" class="new" title="25 (nombre) (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">25</a> </td> <td align="right">6<b>25</b> </td></tr> <tr> <td align="right">625 </td> <td align="right">390<b>625</b> </td></tr> <tr> <td align="right">90625 </td> <td align="right">82128<b>90625</b> </td></tr> <tr> <td align="right">890625 </td> <td align="right">793212<b>890625</b> </td></tr> <tr> <td align="right">2890625 </td> <td align="right">835571<b>2890625</b> </td></tr> <tr> <td align="right">12890625 </td> <td align="right">1661682<b>12890625</b> </td></tr> <tr> <td align="right">212890625 </td> <td align="right">45322418<b>212890625</b> </td></tr> <tr> <td align="right">8212890625 </td> <td align="right">6745157241<b>8212890625</b> </td></tr> <tr> <td align="right">18212890625 </td> <td align="right">3317093849<b>18212890625</b> </td></tr> <tr> <td align="right">918212890625 </td> <td align="right">843114912509<b>918212890625</b> </td></tr> <tr> <td align="right">9918212890625 </td> <td align="right">9837094694375<b>9918212890625</b> </td></tr> <tr> <td align="right">59918212890625 </td> <td align="right">35901922360062<b>59918212890625</b> </td></tr> <tr> <td align="right">259918212890625 </td> <td align="right">67557477392256<b>259918212890625</b> </td></tr> <tr> <td align="right">6259918212890625 </td> <td align="right">3918657603207975<b>6259918212890625</b> </td></tr> <tr> <td align="right">56259918212890625 </td> <td align="right">31651783973211422<b>56259918212890625</b> </td></tr> <tr> <td align="right">256259918212890625 </td> <td align="right">65669145682477392<b>256259918212890625</b> </td></tr> <tr> <td align="right">2256259918212890625 </td> <td align="right">509070881853403989<b>2256259918212890625</b> </td></tr> <tr> <td align="right">92256259918212890625 </td> <td align="right">85112174940968543523<b>92256259918212890625</b> </td></tr> <tr> <td align="right">392256259918212890625 </td> <td align="right">153864973445024588727<b>392256259918212890625</b> </td></tr> <tr> <td align="right">7392256259918212890625 </td> <td align="right">5464545261230000505747<b>7392256259918212890625</b> </td></tr> <tr> <td align="right">77392256259918212890625 </td> <td align="right">59895613290008498097449<b>77392256259918212890625</b> </td></tr> <tr> <td align="right">977392256259918212890625 </td> <td align="right">955295622596853633012869<b>977392256259918212890625</b> </td></tr> <tr> <td align="right">9977392256259918212890625 </td> <td align="right">9954835623527538146504411<b>9977392256259918212890625</b> </td></tr> <tr> <td align="right">19977392256259918212890625 </td> <td align="right">3990962013604737457228566<b>19977392256259918212890625</b> </td></tr> <tr> <td align="right">619977392256259918212890625 </td> <td align="right">384371966908872375601191606<b>619977392256259918212890625</b> </td></tr> <tr> <td align="right">6619977392256259918212890625 </td> <td align="right">4382410067398399139415587910<b>6619977392256259918212890625</b> </td></tr> <tr> <td align="right">106619977392256259918212890625 </td> <td align="right">11367819579125235975036734004<b>106619977392256259918212890625</b> </td></tr> <tr> <td align="right">4106619977392256259918212890625 </td> <td align="right">1686432763871717531532073985900<b>4106619977392256259918212890625</b> </td></tr> <tr> <td align="right">9004106619977392256259918212890625 </td> <td align="right">8107393602392069932985384315277110<b>9004106619977392256259918212890625</b> </td></tr></tbody></table> <table border="2"> <tbody><tr bgcolor="#90ee90"> <th><i>n</i> </th> <th><i>n</i><sup>2</sup> </th></tr> <tr> <td align="right"><a href="/w/index.php?title=6_(nombre)&action=edit&redlink=1" class="new" title="6 (nombre) (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">6</a> </td> <td align="right">3<b>6</b> </td></tr> <tr> <td align="right"><a href="/w/index.php?title=76_(nombre)&action=edit&redlink=1" class="new" title="76 (nombre) (ទំព័រនេះមិនទាន់មាននៅឡើយទេ)">76</a> </td> <td align="right">57<b>76</b> </td></tr> <tr> <td align="right">376 </td> <td align="right">141<b>376</b> </td></tr> <tr> <td align="right">9376 </td> <td align="right">8790<b>9376</b> </td></tr> <tr> <td align="right">109376 </td> <td align="right">11963<b>109376</b> </td></tr> <tr> <td align="right">7109376 </td> <td align="right">5054322<b>7109376</b> </td></tr> <tr> <td align="right">87109376 </td> <td align="right">75880433<b>87109376</b> </td></tr> <tr> <td align="right">787109376 </td> <td align="right">619541169<b>787109376</b> </td></tr> <tr> <td align="right">1787109376 </td> <td align="right">319375992<b>1787109376</b> </td></tr> <tr> <td align="right">81787109376 </td> <td align="right">66891312600<b>81787109376</b> </td></tr> <tr> <td align="right">40081787109376 </td> <td align="right">16065496578813<b>40081787109376</b> </td></tr> <tr> <td align="right">740081787109376 </td> <td align="right">547721051611007<b>740081787109376</b> </td></tr> <tr> <td align="right">3740081787109376 </td> <td align="right">1398821177426726<b>3740081787109376</b> </td></tr> <tr> <td align="right">43740081787109376 </td> <td align="right">19131947547430173<b>43740081787109376</b> </td></tr> <tr> <td align="right">743740081787109376 </td> <td align="right">553149309256696143<b>743740081787109376</b> </td></tr> <tr> <td align="right">7743740081787109376 </td> <td align="right">5996551045427622740<b>7743740081787109376</b> </td></tr> <tr> <td align="right">607743740081787109376 </td> <td align="right">369352453608598807478<b>607743740081787109376</b> </td></tr> <tr> <td align="right">2607743740081787109376 </td> <td align="right">680032741393574724498<b>2607743740081787109376</b> </td></tr> <tr> <td align="right">22607743740081787109376 </td> <td align="right">5111100770172072316200<b>22607743740081787109376</b> </td></tr> <tr> <td align="right">80022607743740081787109376 </td> <td align="right">64036177501084901031447317<b>80022607743740081787109376</b> </td></tr> <tr> <td align="right">380022607743740081787109376 </td> <td align="right">144417182396352539175410357<b>380022607743740081787109376</b> </td></tr> <tr> <td align="right">3380022607743740081787109376 </td> <td align="right">1142455282885879302989806661<b>3380022607743740081787109376</b> </td></tr> <tr> <td align="right">893380022607743740081787109376 </td> <td align="right">798127864794612716138610952755<b>893380022607743740081787109376</b> </td></tr> <tr> <td align="right">5893380022607743740081787109376 </td> <td align="right">3473192809087205011695648204651<b>5893380022607743740081787109376</b> </td></tr> <tr> <td align="right">995893380022607743740081787109376 </td> <td align="right">991803624372854204655478894958610<b>995893380022607743740081787109376</b> </td></tr></tbody></table>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1&useformat=desktop" alt="" width="1" height="1" style="border: none; position: absolute;"></noscript> <div class="printfooter" data-nosnippet="">បានពី "<a dir="ltr" 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