142857 – Wikipedie

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role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-titlebar-toc" class="vector-dropdown-checkbox " aria-label="Přepnout obsah" > <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">Přepnout obsah</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">142857</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="Přejděte k článku v jiném jazyce. Je dostupný v 26 jazycích" > <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-26" 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">26 jazyků</span> </label> <div class="vector-dropdown-content"> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="interlanguage-link interwiki-da mw-list-item"><a href="https://da.wikipedia.org/wiki/142857" title="142857 – dánština" lang="da" hreflang="da" data-title="142857" data-language-autonym="Dansk" data-language-local-name="dánština" 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/142857" title="142857 – němčina" lang="de" hreflang="de" data-title="142857" data-language-autonym="Deutsch" data-language-local-name="němčina" 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/142857" title="142857 – řečtina" lang="el" hreflang="el" data-title="142857" data-language-autonym="Ελληνικά" data-language-local-name="řečtina" 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/142857" title="142857 – angličtina" lang="en" hreflang="en" data-title="142857" data-language-autonym="English" data-language-local-name="angličtina" class="interlanguage-link-target"><span>English</span></a></li><li class="interlanguage-link interwiki-es mw-list-item"><a href="https://es.wikipedia.org/wiki/142_857" title="142 857 – španělština" lang="es" hreflang="es" data-title="142 857" data-language-autonym="Español" data-language-local-name="španělština" class="interlanguage-link-target"><span>Español</span></a></li><li class="interlanguage-link interwiki-fa mw-list-item"><a href="https://fa.wikipedia.org/wiki/%DB%B1%DB%B4%DB%B2%DB%B8%DB%B5%DB%B7" title="۱۴۲۸۵۷ – perština" lang="fa" hreflang="fa" data-title="۱۴۲۸۵۷" data-language-autonym="فارسی" data-language-local-name="perština" class="interlanguage-link-target"><span>فارسی</span></a></li><li class="interlanguage-link interwiki-fr mw-list-item"><a href="https://fr.wikipedia.org/wiki/142_857_(nombre)" title="142 857 (nombre) – francouzština" lang="fr" hreflang="fr" data-title="142 857 (nombre)" data-language-autonym="Français" data-language-local-name="francouzština" class="interlanguage-link-target"><span>Français</span></a></li><li class="interlanguage-link interwiki-hi mw-list-item"><a href="https://hi.wikipedia.org/wiki/142857_(%E0%A4%B8%E0%A4%82%E0%A4%96%E0%A5%8D%E0%A4%AF%E0%A4%BE)" title="142857 (संख्या) – hindština" lang="hi" hreflang="hi" data-title="142857 (संख्या)" data-language-autonym="हिन्दी" data-language-local-name="hindština" class="interlanguage-link-target"><span>हिन्दी</span></a></li><li class="interlanguage-link interwiki-hu mw-list-item"><a href="https://hu.wikipedia.org/wiki/142857_(sz%C3%A1m)" title="142857 (szám) – maďarština" lang="hu" hreflang="hu" data-title="142857 (szám)" data-language-autonym="Magyar" data-language-local-name="maďarština" class="interlanguage-link-target"><span>Magyar</span></a></li><li class="interlanguage-link interwiki-id mw-list-item"><a href="https://id.wikipedia.org/wiki/142.857_(angka)" title="142.857 (angka) – indonéština" lang="id" hreflang="id" data-title="142.857 (angka)" data-language-autonym="Bahasa Indonesia" data-language-local-name="indonéština" class="interlanguage-link-target"><span>Bahasa Indonesia</span></a></li><li class="interlanguage-link interwiki-it mw-list-item"><a href="https://it.wikipedia.org/wiki/142857" title="142857 – italština" lang="it" hreflang="it" data-title="142857" data-language-autonym="Italiano" data-language-local-name="italština" 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/142857" title="142857 – japonština" lang="ja" hreflang="ja" data-title="142857" data-language-autonym="日本語" data-language-local-name="japonština" class="interlanguage-link-target"><span>日本語</span></a></li><li class="interlanguage-link interwiki-ko mw-list-item"><a href="https://ko.wikipedia.org/wiki/142,857" title="142,857 – korejština" lang="ko" hreflang="ko" data-title="142,857" data-language-autonym="한국어" data-language-local-name="korejština" class="interlanguage-link-target"><span>한국어</span></a></li><li class="interlanguage-link interwiki-lv mw-list-item"><a href="https://lv.wikipedia.org/wiki/142857_(skaitlis)" title="142857 (skaitlis) – lotyština" lang="lv" hreflang="lv" data-title="142857 (skaitlis)" data-language-autonym="Latviešu" data-language-local-name="lotyština" class="interlanguage-link-target"><span>Latviešu</span></a></li><li class="interlanguage-link interwiki-no mw-list-item"><a href="https://no.wikipedia.org/wiki/142857" title="142857 – norština (bokmål)" lang="nb" hreflang="nb" data-title="142857" data-language-autonym="Norsk bokmål" data-language-local-name="norština (bokmål)" class="interlanguage-link-target"><span>Norsk bokmål</span></a></li><li class="interlanguage-link interwiki-pt mw-list-item"><a href="https://pt.wikipedia.org/wiki/142857_(n%C3%BAmero)" title="142857 (número) – portugalština" lang="pt" hreflang="pt" data-title="142857 (número)" data-language-autonym="Português" data-language-local-name="portugalština" 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/142857_(num%C4%83r)" title="142857 (număr) – rumunština" lang="ro" hreflang="ro" data-title="142857 (număr)" data-language-autonym="Română" data-language-local-name="rumunština" 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/142_857_(%D1%87%D0%B8%D1%81%D0%BB%D0%BE)" title="142 857 (число) – ruština" lang="ru" hreflang="ru" data-title="142 857 (число)" data-language-autonym="Русский" data-language-local-name="ruština" class="interlanguage-link-target"><span>Русский</span></a></li><li class="interlanguage-link interwiki-sr mw-list-item"><a href="https://sr.wikipedia.org/wiki/142857" title="142857 – srbština" lang="sr" hreflang="sr" data-title="142857" data-language-autonym="Српски / srpski" data-language-local-name="srbština" 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/142857_(tal)" title="142857 (tal) – švédština" lang="sv" hreflang="sv" data-title="142857 (tal)" data-language-autonym="Svenska" data-language-local-name="švédština" class="interlanguage-link-target"><span>Svenska</span></a></li><li class="interlanguage-link interwiki-ta mw-list-item"><a href="https://ta.wikipedia.org/wiki/142857_(%E0%AE%8E%E0%AE%A3%E0%AF%8D)" title="142857 (எண்) – tamilština" lang="ta" hreflang="ta" data-title="142857 (எண்)" data-language-autonym="தமிழ்" data-language-local-name="tamilština" 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/142857" title="142857 – thajština" lang="th" hreflang="th" data-title="142857" data-language-autonym="ไทย" data-language-local-name="thajština" class="interlanguage-link-target"><span>ไทย</span></a></li><li class="interlanguage-link interwiki-tr mw-list-item"><a href="https://tr.wikipedia.org/wiki/142857" title="142857 – turečtina" lang="tr" hreflang="tr" data-title="142857" data-language-autonym="Türkçe" data-language-local-name="turečtina" class="interlanguage-link-target"><span>Türkçe</span></a></li><li class="interlanguage-link interwiki-ur mw-list-item"><a href="https://ur.wikipedia.org/wiki/142857_(%D8%B9%D8%AF%D8%AF)" title="142857 (عدد) – urdština" lang="ur" hreflang="ur" data-title="142857 (عدد)" data-language-autonym="اردو" data-language-local-name="urdština" class="interlanguage-link-target"><span>اردو</span></a></li><li class="interlanguage-link interwiki-vi mw-list-item"><a href="https://vi.wikipedia.org/wiki/142857" title="142857 – vietnamština" lang="vi" hreflang="vi" data-title="142857" data-language-autonym="Tiếng Việt" data-language-local-name="vietnamština" class="interlanguage-link-target"><span>Tiếng Việt</span></a></li><li class="interlanguage-link interwiki-zh mw-list-item"><a href="https://zh.wikipedia.org/wiki/142857" title="142857 – čínština" lang="zh" hreflang="zh" data-title="142857" data-language-autonym="中文" data-language-local-name="čínština" 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/Q846329#sitelinks-wikipedia" title="Editovat mezijazykové odkazy" class="wbc-editpage">Upravit odkazy</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="Jmenné prostory"> <div id="p-associated-pages" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-associated-pages" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-nstab-main" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/142857" title="Zobrazit obsahovou stránku [c]" accesskey="c"><span>Článek</span></a></li><li id="ca-talk" class="vector-tab-noicon mw-list-item"><a href="/wiki/Diskuse:142857" rel="discussion" title="Diskuse ke stránce [t]" accesskey="t"><span>Diskuse</span></a></li> </ul> </div> </div> <div id="vector-variants-dropdown" class="vector-dropdown emptyPortlet" > <input type="checkbox" id="vector-variants-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-variants-dropdown" class="vector-dropdown-checkbox " aria-label="Změnit variantu jazyka" > <label id="vector-variants-dropdown-label" for="vector-variants-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">čeština</span> </label> <div class="vector-dropdown-content"> <div id="p-variants" class="vector-menu mw-portlet mw-portlet-variants emptyPortlet" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> </ul> </div> </div> </div> </div> </nav> </div> <div id="right-navigation" class="vector-collapsible"> <nav aria-label="Zobrazení"> <div id="p-views" class="vector-menu vector-menu-tabs mw-portlet mw-portlet-views" > <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-view" class="selected vector-tab-noicon mw-list-item"><a href="/wiki/142857"><span>Číst</span></a></li><li id="ca-ve-edit" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=142857&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-edit" class="collapsible vector-tab-noicon mw-list-item"><a href="/w/index.php?title=142857&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-history" class="vector-tab-noicon mw-list-item"><a href="/w/index.php?title=142857&action=history" title="Starší verze této stránky. [h]" accesskey="h"><span>Zobrazit historii</span></a></li> </ul> </div> </div> </nav> <nav class="vector-page-tools-landmark" aria-label="Nástroje ke stránce"> <div id="vector-page-tools-dropdown" class="vector-dropdown vector-page-tools-dropdown" > <input type="checkbox" id="vector-page-tools-dropdown-checkbox" role="button" aria-haspopup="true" data-event-name="ui.dropdown-vector-page-tools-dropdown" class="vector-dropdown-checkbox " aria-label="Nástroje" > <label id="vector-page-tools-dropdown-label" for="vector-page-tools-dropdown-checkbox" class="vector-dropdown-label cdx-button cdx-button--fake-button cdx-button--fake-button--enabled cdx-button--weight-quiet" aria-hidden="true" ><span class="vector-dropdown-label-text">Nástroje</span> </label> <div class="vector-dropdown-content"> <div id="vector-page-tools-unpinned-container" class="vector-unpinned-container"> <div id="vector-page-tools" class="vector-page-tools vector-pinnable-element"> <div class="vector-pinnable-header vector-page-tools-pinnable-header vector-pinnable-header-unpinned" data-feature-name="page-tools-pinned" data-pinnable-element-id="vector-page-tools" data-pinned-container-id="vector-page-tools-pinned-container" data-unpinned-container-id="vector-page-tools-unpinned-container" > <div class="vector-pinnable-header-label">Nástroje</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-page-tools.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-page-tools.unpin">skrýt</button> </div> <div id="p-cactions" class="vector-menu mw-portlet mw-portlet-cactions emptyPortlet vector-has-collapsible-items" title="Další možnosti" > <div class="vector-menu-heading"> Akce </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="ca-more-view" class="selected vector-more-collapsible-item mw-list-item"><a href="/wiki/142857"><span>Číst</span></a></li><li id="ca-more-ve-edit" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=142857&veaction=edit" title="Editovat tuto stránku [v]" accesskey="v"><span>Editovat</span></a></li><li id="ca-more-edit" class="collapsible vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=142857&action=edit" title="Editovat zdrojový kód této stránky [e]" accesskey="e"><span>Editovat zdroj</span></a></li><li id="ca-more-history" class="vector-more-collapsible-item mw-list-item"><a href="/w/index.php?title=142857&action=history"><span>Zobrazit historii</span></a></li> </ul> </div> </div> <div id="p-tb" class="vector-menu mw-portlet mw-portlet-tb" > <div class="vector-menu-heading"> Obecné </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="t-whatlinkshere" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Co_odkazuje_na/142857" title="Seznam všech wikistránek, které sem odkazují [j]" accesskey="j"><span>Odkazuje sem</span></a></li><li id="t-recentchangeslinked" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Souvisej%C3%ADc%C3%AD_zm%C4%9Bny/142857" rel="nofollow" title="Nedávné změny stránek, na které je odkazováno [k]" accesskey="k"><span>Související změny</span></a></li><li id="t-upload" class="mw-list-item"><a href="//commons.wikimedia.org/wiki/Special:UploadWizard?uselang=cs" title="Nahrát obrázky či jiná multimédia [u]" accesskey="u"><span>Načíst soubor</span></a></li><li id="t-specialpages" class="mw-list-item"><a href="/wiki/Speci%C3%A1ln%C3%AD:Speci%C3%A1ln%C3%AD_str%C3%A1nky" title="Seznam všech speciálních stránek [q]" accesskey="q"><span>Speciální stránky</span></a></li><li id="t-permalink" class="mw-list-item"><a href="/w/index.php?title=142857&oldid=23640228" title="Trvalý odkaz na současnou verzi této stránky"><span>Trvalý odkaz</span></a></li><li id="t-info" class="mw-list-item"><a href="/w/index.php?title=142857&action=info" title="Více informací o této stránce"><span>Informace o stránce</span></a></li><li id="t-cite" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Citovat&page=142857&id=23640228&wpFormIdentifier=titleform" title="Informace o tom, jak citovat tuto stránku"><span>Citovat stránku</span></a></li><li id="t-urlshortener" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:UrlShortener&url=https%3A%2F%2Fcs.wikipedia.org%2Fwiki%2F142857"><span>Získat zkrácené URL</span></a></li><li id="t-urlshortener-qrcode" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:QrCode&url=https%3A%2F%2Fcs.wikipedia.org%2Fwiki%2F142857"><span>Stáhnout QR kód</span></a></li> </ul> </div> </div> <div id="p-coll-print_export" class="vector-menu mw-portlet mw-portlet-coll-print_export" > <div class="vector-menu-heading"> Tisk/export </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li id="coll-create_a_book" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:Kniha&bookcmd=book_creator&referer=142857"><span>Vytvořit knihu</span></a></li><li id="coll-download-as-rl" class="mw-list-item"><a href="/w/index.php?title=Speci%C3%A1ln%C3%AD:DownloadAsPdf&page=142857&action=show-download-screen"><span>Stáhnout jako PDF</span></a></li><li id="t-print" class="mw-list-item"><a href="/w/index.php?title=142857&printable=yes" title="Tato stránka v podobě vhodné k tisku [p]" accesskey="p"><span>Verze k tisku</span></a></li> </ul> </div> </div> <div id="p-wikibase-otherprojects" class="vector-menu mw-portlet mw-portlet-wikibase-otherprojects" > <div class="vector-menu-heading"> Na jiných projektech </div> <div class="vector-menu-content"> <ul class="vector-menu-content-list"> <li class="wb-otherproject-link wb-otherproject-commons mw-list-item"><a href="https://commons.wikimedia.org/wiki/Category:142857_(number)" hreflang="en"><span>Wikimedia Commons</span></a></li><li id="t-wikibase" class="wb-otherproject-link wb-otherproject-wikibase-dataitem mw-list-item"><a href="https://www.wikidata.org/wiki/Special:EntityPage/Q846329" title="Odkaz na propojenou položku datového úložiště [g]" accesskey="g"><span>Položka Wikidat</span></a></li> </ul> </div> </div> </div> </div> </div> </div> </nav> </div> </div> </div> <div class="vector-column-end"> <div class="vector-sticky-pinned-container"> <nav class="vector-page-tools-landmark" aria-label="Nástroje ke stránce"> <div id="vector-page-tools-pinned-container" class="vector-pinned-container"> </div> </nav> <nav class="vector-appearance-landmark" aria-label="Vzhled"> <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">Vzhled</div> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-pin-button" data-event-name="pinnable-header.vector-appearance.pin">přesunout do postranního panelu</button> <button class="vector-pinnable-header-toggle-button vector-pinnable-header-unpin-button" data-event-name="pinnable-header.vector-appearance.unpin">skrýt</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">Z Wikipedie, otevřené encyklopedie</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="cs" dir="ltr"><table class="infobox" style="width: 22em; font-size: 88%; text-align: left; line-height: 1.5em;"> <tbody><tr> <th colspan="2" style="font-size: 125%; text-align: center"><table style="width: 100%"><tbody><tr valign="middle"> <td style="text-align:center; white-space:nowrap;"><span class="Unicode">←</span> 142 856</td> <td style="text-align:center; white-space:nowrap;">142 857</td> <td style="text-align:center; white-space:nowrap;">142 858 <span class="Unicode">→</span></td> </tr></tbody></table> </th></tr> <tr> <td colspan="2"> </td></tr> <tr> <th style="text-align: left;"><a href="/wiki/Cel%C3%A9_%C4%8D%C3%ADslo" title="Celé číslo">Celé číslo</a> </th> <td>142 857<br />sto čtyřicet dva tisíc osm set padesát sedm </td></tr> <tr> <th style="text-align: left;"><a href="/wiki/Prvo%C4%8D%C3%ADseln%C3%BD_rozklad" title="Prvočíselný rozklad">Rozklad</a> </th> <td>3<sup>3</sup> · 11 · 13 · 37 </td></tr> <tr> <th style="text-align: left;"><a href="/wiki/D%C4%9Blen%C3%AD" title="Dělení">Dělitelé</a> </th> <td>1, 3, 9, 11, 13, 27, 33, 37, 39, 99, 111, 117, 143, 297, 333, 351, 407, 429, 481, 999, 1221, 1287, 1443, 3663, 3861, 4329, 5291, 10989, 12987, 15873, 47619, 142857 </td></tr> <tr> <th style="text-align: left;"><a href="/wiki/%C5%98%C3%ADmsk%C3%A9_%C4%8D%C3%ADslice" title="Římské číslice">Římskými číslicemi</a> </th> <td> </td></tr> <tr> <th style="text-align: left;"><a href="/wiki/Dvojkov%C3%A1_soustava" title="Dvojková soustava">Dvojkově</a> </th> <td>100010111000001001 </td></tr> <tr> <th style="text-align: left;"><a href="/wiki/Osmi%C4%8Dkov%C3%A1_soustava" title="Osmičková soustava">Osmičkově</a> </th> <td>427011 </td></tr> <tr> <th style="text-align: left;"><a href="/wiki/%C5%A0estn%C3%A1ctkov%C3%A1_soustava" title="Šestnáctková soustava">Šestnáctkově</a> </th> <td>22E09 </td></tr></tbody></table> <p><b>142857</b> je přirozené číslo. Představuje šest <a href="/wiki/Perioda_(matematika)" title="Perioda (matematika)">periodických</a> číslic čísla <b>1/7</b>, <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 0{,}{\overline {142857}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mover> <mn>142857</mn> <mo accent="false">¯</mo> </mover> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle 0{,}{\overline {142857}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/fca8fae614b97ea277022b6e83a1ede66334c84c" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:8.899ex; height:3.343ex;" alt="{\displaystyle 0{,}{\overline {142857}}}"></span>, jedná se pravděpodobně o nejznámější cyklické číslo v <a href="/wiki/Des%C3%ADtkov%C3%A1_soustava" title="Desítková soustava">desítkové soustavě</a>. Pokud je <a href="/wiki/N%C3%A1soben%C3%AD" title="Násobení">vynásobeno</a> 2, 3, 4, 5, nebo 6, výsledek je <a href="/w/index.php?title=Cyklick%C3%A1_permutace&action=edit&redlink=1" class="new" title="Cyklická permutace (stránka neexistuje)">cyklická permutace</a> sebe sama a koresponduje s opakujícími se číslicemi <b>2/7</b>, <b>3/7</b>, <b>4/7</b>, <b>5/7</b>, a <b>6/7</b>. </p> <div class="mw-heading mw-heading2"><h2 id="Výpočty"><span id="V.C3.BDpo.C4.8Dty"></span>Výpočty</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=142857&veaction=edit&section=1" title="Editace sekce: Výpočty" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=142857&action=edit&section=1" title="Editovat zdrojový kód sekce Výpočty"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <table class="wikitable"> <tbody><tr> <td>142857 × 1 = 142857</td> <td>1 ÷ 7 = 0,<span style="text-decoration: overline;">142857</span> </td></tr> <tr> <td>142857 × 2 = 285714</td> <td>2 ÷ 7 = 0,<span style="text-decoration: overline;">285714</span> </td></tr> <tr> <td>142857 × 3 = 428571</td> <td>3 ÷ 7 = 0,<span style="text-decoration: overline;">428571</span> </td></tr> <tr> <td>142857 × 4 = 571428</td> <td>4 ÷ 7 = 0,<span style="text-decoration: overline;">571428</span> </td></tr> <tr> <td>142857 × 5 = 714285</td> <td>5 ÷ 7 = 0,<span style="text-decoration: overline;">714285</span> </td></tr> <tr> <td>142857 × 6 = 857142</td> <td>6 ÷ 7 = 0,<span style="text-decoration: overline;">857142</span> </td></tr> <tr> <td>142857 × 7 = 999999</td> <td>7 ÷ 7 = <a href="/w/index.php?title=0,999...&action=edit&redlink=1" class="new" title="0,999... (stránka neexistuje)">0,<span style="text-decoration: overline;">999999</span></a> = 1 </td></tr> <tr> <td rowspan="2"><small>(viz dále)</small></td> <td>8 ÷ 7 = 1,<span style="text-decoration: overline;">142857</span> </td></tr> <tr> <td>9 ÷ 7 = 1,<span style="text-decoration: overline;">285714</span> </td></tr></tbody></table> <p>Pokud se 142857 vynásobí číslem větším než 7, existuje poměrně jednoduchý proces jak dostat opět cyklickou <a href="/wiki/Permutace" title="Permutace">permutaci</a> čísla 142857. Sečtením pravých šesti číslic se zbylými číslicemi a opakováním, dokud nezůstane pouze 6 číslic. Vznikne opět cyklická permutace 142857, např.: </p> <dl><dd>142857 × 8 = 1142856</dd> <dd>1 + 142856 = 142857</dd></dl> <dl><dd>142857 × 815 = 116428455</dd> <dd>116 + 428455 = 428571</dd></dl> <dl><dd>142857<sup>2</sup> = 142857 × 142857 = 20408122449</dd> <dd>20408 + 122449 = 142857</dd></dl> <p>Násobením násobkem čísla 7 vyjde opět po použití předešlého procesu číslo 999999. </p> <dl><dd>142857 × 7<sup>4</sup> = 342999657</dd> <dd>342 + 999657 = 999999</dd></dl> <p>Rozdíl kvadrátů prvního a druhého trojčíslí (kterékoli cyklické permutace 142857) dá (v <a href="/wiki/Absolutn%C3%AD_hodnota" title="Absolutní hodnota">absolutní hodnotě</a>) opět cyklickou permutaci, např.: </p> <dl><dd>857<sup>2</sup> − 142<sup>2</sup> = 734449 − 20164 = 714285</dd></dl> <div class="mw-heading mw-heading2"><h2 id="1/7_jako_nekonečná_řada"><span id="1.2F7_jako_nekone.C4.8Dn.C3.A1_.C5.99ada"></span>1/7 jako nekonečná řada</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=142857&veaction=edit&section=2" title="Editace sekce: 1/7 jako nekonečná řada" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=142857&action=edit&section=2" title="Editovat zdrojový kód sekce 1/7 jako nekonečná řada"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <p>Existuje zajímavý model, podle kterého jde tato nekonečná řada sestavit. Krom toho, že se 1/7 skládá z opakování 142857, lze číslo napsat i s využitím zdvojení, řazení a sčítání, která dává 1/7. </p><p><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 {\begin{aligned}1/7\ &=0{,}142857142857142857\ldots \\[6pt]&=0{,}14+0{,}0028+0{,}000056+0{,}00000112+0{,}0000000224+0{,}000000000448+0{,}00000000000896+\cdots \\[6pt]&={\frac {14}{100}}+{\frac {28}{100^{2}}}+{\frac {56}{100^{3}}}+{\frac {112}{100^{4}}}+{\frac {224}{100^{5}}}+\cdots +{\frac {7\times 2^{N}}{100^{N}}}+\cdots \\[6pt]&=\left({\frac {7}{50}}+{\frac {7}{50^{2}}}+{\frac {7}{50^{3}}}+{\frac {7}{50^{4}}}+{\frac {7}{50^{5}}}+\cdots +{\frac {7}{50^{N}}}+\cdots \right)\\[6pt]&=\sum _{k=1}^{\infty }{\frac {7}{50^{k}}}\end{aligned}}}"> <semantics> <mrow class="MJX-TeXAtom-ORD"> <mstyle displaystyle="true" scriptlevel="0"> <mrow class="MJX-TeXAtom-ORD"> <mtable columnalign="right left right left right left right left right left right left" rowspacing="0.9em 0.9em 0.9em 0.9em 0.3em" columnspacing="0em 2em 0em 2em 0em 2em 0em 2em 0em 2em 0em" displaystyle="true"> <mtr> <mtd> <mn>1</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>/</mo> </mrow> <mn>7</mn> <mtext> </mtext> </mtd> <mtd> <mi></mi> <mo>=</mo> <mn>0,142</mn> <mn>857142857142857</mn> <mo>…</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mn>0</mn> <mrow class="MJX-TeXAtom-ORD"> <mo>,</mo> </mrow> <mn>14</mn> <mo>+</mo> <mn>0,002</mn> <mn>8</mn> <mo>+</mo> <mn>0,000</mn> <mn>056</mn> <mo>+</mo> <mn>0,000</mn> <mn>00112</mn> <mo>+</mo> <mn>0,000</mn> <mn>0000224</mn> <mo>+</mo> <mn>0,000</mn> <mn>000000448</mn> <mo>+</mo> <mn>0,000</mn> <mn>00000000896</mn> <mo>+</mo> <mo>⋯</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>14</mn> <mn>100</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>28</mn> <msup> <mn>100</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>56</mn> <msup> <mn>100</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>112</mn> <msup> <mn>100</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>224</mn> <msup> <mn>100</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mrow> <mn>7</mn> <mo>×</mo> <msup> <mn>2</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mrow> <msup> <mn>100</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <mrow> <mo>(</mo> <mrow> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <mn>50</mn> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <msup> <mn>50</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>2</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <msup> <mn>50</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>3</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <msup> <mn>50</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>4</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <msup> <mn>50</mn> <mrow class="MJX-TeXAtom-ORD"> <mn>5</mn> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> <mo>+</mo> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <msup> <mn>50</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>N</mi> </mrow> </msup> </mfrac> </mrow> <mo>+</mo> <mo>⋯</mo> </mrow> <mo>)</mo> </mrow> </mtd> </mtr> <mtr> <mtd /> <mtd> <mi></mi> <mo>=</mo> <munderover> <mo>∑</mo> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> <mo>=</mo> <mn>1</mn> </mrow> <mrow class="MJX-TeXAtom-ORD"> <mi mathvariant="normal">∞</mi> </mrow> </munderover> <mrow class="MJX-TeXAtom-ORD"> <mfrac> <mn>7</mn> <msup> <mn>50</mn> <mrow class="MJX-TeXAtom-ORD"> <mi>k</mi> </mrow> </msup> </mfrac> </mrow> </mtd> </mtr> </mtable> </mrow> </mstyle> </mrow> <annotation encoding="application/x-tex">{\displaystyle {\begin{aligned}1/7\ &=0{,}142857142857142857\ldots \\[6pt]&=0{,}14+0{,}0028+0{,}000056+0{,}00000112+0{,}0000000224+0{,}000000000448+0{,}00000000000896+\cdots \\[6pt]&={\frac {14}{100}}+{\frac {28}{100^{2}}}+{\frac {56}{100^{3}}}+{\frac {112}{100^{4}}}+{\frac {224}{100^{5}}}+\cdots +{\frac {7\times 2^{N}}{100^{N}}}+\cdots \\[6pt]&=\left({\frac {7}{50}}+{\frac {7}{50^{2}}}+{\frac {7}{50^{3}}}+{\frac {7}{50^{4}}}+{\frac {7}{50^{5}}}+\cdots +{\frac {7}{50^{N}}}+\cdots \right)\\[6pt]&=\sum _{k=1}^{\infty }{\frac {7}{50^{k}}}\end{aligned}}}</annotation> </semantics> </math></span><img src="https://wikimedia.org/api/rest_v1/media/math/render/svg/a4dc8398fbb76337aa3eae3656b67cd17caccdc4" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -14.874ex; margin-bottom: -0.297ex; width:108.287ex; height:31.509ex;" alt="{\displaystyle {\begin{aligned}1/7\ &=0{,}142857142857142857\ldots \\[6pt]&=0{,}14+0{,}0028+0{,}000056+0{,}00000112+0{,}0000000224+0{,}000000000448+0{,}00000000000896+\cdots \\[6pt]&={\frac {14}{100}}+{\frac {28}{100^{2}}}+{\frac {56}{100^{3}}}+{\frac {112}{100^{4}}}+{\frac {224}{100^{5}}}+\cdots +{\frac {7\times 2^{N}}{100^{N}}}+\cdots \\[6pt]&=\left({\frac {7}{50}}+{\frac {7}{50^{2}}}+{\frac {7}{50^{3}}}+{\frac {7}{50^{4}}}+{\frac {7}{50^{5}}}+\cdots +{\frac {7}{50^{N}}}+\cdots \right)\\[6pt]&=\sum _{k=1}^{\infty }{\frac {7}{50^{k}}}\end{aligned}}}"></span> </p><p>Každý člen je dvojnásobek předchozího posunutý o dvě místa doprava. </p> <div class="mw-heading mw-heading2"><h2 id="Externí_odkazy"><span id="Extern.C3.AD_odkazy"></span>Externí odkazy</h2><span class="mw-editsection"><span class="mw-editsection-bracket">[</span><a href="/w/index.php?title=142857&veaction=edit&section=3" title="Editace sekce: Externí odkazy" class="mw-editsection-visualeditor"><span>editovat</span></a><span class="mw-editsection-divider"> | </span><a href="/w/index.php?title=142857&action=edit&section=3" title="Editovat zdrojový kód sekce Externí odkazy"><span>editovat zdroj</span></a><span class="mw-editsection-bracket">]</span></span></div> <ul><li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20070821203332/http://www.142857.com/">Stránka čísla 142857</a></li> <li><a rel="nofollow" class="external text" href="https://web.archive.org/web/20090227104724/http://www.jeorgethedodo.com/huh_142857.asp">142857 Kalkulačka</a></li></ul>    </div><noscript><img src="https://login.wikimedia.org/wiki/Special:CentralAutoLogin/start?type=1x1" alt="" width="1" height="1" style="border: 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