{"id":26770,"date":"2022-06-16T06:39:30","date_gmt":"2022-06-16T04:39:30","guid":{"rendered":"https:\/\/mahifi.se\/?page_id=26770"},"modified":"2022-10-06T15:47:22","modified_gmt":"2022-10-06T13:47:22","slug":"fermats-sats","status":"publish","type":"page","link":"https:\/\/mahifi.se\/?page_id=26770","title":{"rendered":"Fermats sats"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"26770\" class=\"elementor elementor-26770\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-f10206d elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"f10206d\" data-element_type=\"section\" data-e-type=\"section\" data-settings=\"{&quot;background_background&quot;:&quot;classic&quot;}\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-aa89980\" data-id=\"aa89980\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-b467801 elementor-widget elementor-widget-heading\" data-id=\"b467801\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<h2 class=\"elementor-heading-title elementor-size-default\">Fermats sats - Det enkla problemet med sv\u00e5r l\u00f6sning<\/h2>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-89ac585 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"89ac585\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-463e22f\" data-id=\"463e22f\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7382a8e elementor-widget elementor-widget-text-editor\" data-id=\"7382a8e\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p><span class=\"katex-eq\" data-katex-display=\"false\"> a^n+b^n\\neq c^n, n&gt;2 \\quad a,b,c,n \\in \\mathbb{N} <\/span> eller det finns inga positiva heltalsl\u00f6sningar som tillfredst\u00e4ller ekvationen <span class=\"katex-eq\" data-katex-display=\"false\"> a^n+b^n=c^n <\/span> om <span class=\"katex-eq\" data-katex-display=\"false\"> n <\/span> \u00e4r st\u00f6rre \u00e4n 2. En mycket enkel sats som de flesta kan f\u00f6rst\u00e5. Det \u00e4r en sats som Pierre de Fermat (1607-1665) formulerade 1637 i marginalen av hans exemplar av Diofantes bok Artihmetica. Fermat p\u00e5stod ocks\u00e5 att hans hade ett bevis f\u00f6r den satsen. Han skrev i marginalen: &#8221;Jag har ett i sanning underbart bevis f\u00f6r detta p\u00e5st\u00e5ende, men marginalen \u00e4r alltf\u00f6r tr\u00e5ng f\u00f6r att rymma detsamma&#8221;. Man har i efterhand f\u00f6rs\u00f6k hitta beviset som Fermat p\u00e5stod sig ha hittat, tyv\u00e4rr har man inte funnit det. Anledningen varf\u00f6r man var s\u00e5 intresserad av det beviset var f\u00f6r att ingen annan under de n\u00e4stkommande 350 \u00e5ren inte kunde bevisa satsen som Fermat slarvigt hade formulerat.\u00a0<\/p><p>Flera matematiker bland annat Leonhard Euler lyckades bevisa att fallet g\u00e4ller f\u00f6r <span class=\"katex-eq\" data-katex-display=\"false\"> n=4 <\/span> och under 1800-talet kunde man ocks\u00e5 visa att det st\u00e4mmer f\u00f6r\u00a0<span style=\"background-color: var(--ast-global-color-4); color: var(--ast-global-color-3); font-size: 1rem;\"><span class=\"katex-eq\" data-katex-display=\"false\"> n=5 <\/span> och\u00a0<\/span><span style=\"background-color: var(--ast-global-color-4); color: var(--ast-global-color-3); font-size: 1rem;\"><span class=\"katex-eq\" data-katex-display=\"false\"> n=7 <\/span>. Problemet var att kunna visa det f\u00f6r samtliga\u00a0<\/span><span style=\"background-color: var(--ast-global-color-4); color: var(--ast-global-color-3); font-size: 1rem;\"><span class=\"katex-eq\" data-katex-display=\"false\"> n&gt;2 <\/span>.\u00a0<\/span><\/p><p><span style=\"background-color: var(--ast-global-color-4); color: var(--ast-global-color-3); font-size: 1rem;\">Andrew Wiles (f\u00f6dd 1953) hittade som ung pojke en bok som beskrev Fermat och hans sats som fortfarande inte var bevisad. Han studerade matematik p\u00e5 det prestigefyllda universitetet Cambridge och blev senare professor p\u00e5 samma universitetet. I slutet av 80-talet b\u00f6rjade Andrew Wiles f\u00f6rs\u00f6ka l\u00f6sa problemet. Under l\u00e5ng tid k\u00e4mpade han med beviset som han dessutom h\u00f6ll i hemlighet. 1993 efter 7 \u00e5r av arbete med beviset presenterade Andrew Wiles vad han trodde var det slutgiltiga beviset f\u00f6r Fermats sats. N\u00e4r matematiker granskade bevisade hittade de ett fel. Det tog Andrew Wiles 1 \u00e5r att r\u00e4tta till felen, 1995 kunde han presentera beviset som accepterades av det matematiska s\u00e4llskapet. Beviset \u00e4r \u00f6ver 200 sidor. Det 350 \u00e5r gamla satsen var s\u00e5ledes bevisad.\u00a0<\/span><\/p><p><span style=\"background-color: var(--ast-global-color-4); color: var(--ast-global-color-3); font-size: 1rem;\">Problemet \u00e4r att matematiken som Andrew Wiles anv\u00e4nde f\u00f6r att bevisa Fermats sats var inte k\u00e4nd under Fermats tid. Det betyder allts\u00e5 att beviset som Wiles presenterade inte kunde vara det som Fermat menade att han hade hittat. Det har spekulerats om Fermat haft n\u00e5got bevis \u00f6verhuvudtaget. Vissa menar att Fermat faktiskt trodde att han hade ett bevis men att det var felaktigt eller att han hade ett bevis som vi \u00e4nnu inte har funnit. Fermat var en mycket beg\u00e5vad matematiker som formulerade och bevisade flera viktiga satser. Efter Wiles bevis har ingen funnit ett annat bevis f\u00f6r Fermats sats. Vi f\u00e5r helt enkelt acceptera att vi kanske aldrig kommer f\u00e5 veta.\u00a0<\/span><\/p><p>\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-50 elementor-top-column elementor-element elementor-element-99eda4a\" data-id=\"99eda4a\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-4c17f7f elementor-widget elementor-widget-image\" data-id=\"4c17f7f\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img fetchpriority=\"high\" decoding=\"async\" width=\"299\" height=\"400\" src=\"https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Pierre_de_Fermat.jpg\" class=\"attachment-large size-large wp-image-26788\" alt=\"\" srcset=\"https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Pierre_de_Fermat.jpg 299w, https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Pierre_de_Fermat-224x300.jpg 224w\" sizes=\"(max-width: 299px) 100vw, 299px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-175a320 elementor-widget elementor-widget-text-editor\" data-id=\"175a320\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: center;\">Pierre de Fermat formulerade Fermats sats\u00a0<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4747add elementor-widget elementor-widget-image\" data-id=\"4747add\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"1152\" height=\"1536\" src=\"https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Andrew_wiles1-3-1152x1536.jpeg\" class=\"attachment-1536x1536 size-1536x1536 wp-image-26008\" alt=\"\" srcset=\"https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Andrew_wiles1-3-1152x1536.jpeg 1152w, https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Andrew_wiles1-3-225x300.jpeg 225w, https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Andrew_wiles1-3-768x1024.jpeg 768w, https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Andrew_wiles1-3-1536x2048.jpeg 1536w, https:\/\/mahifi.se\/wp-content\/uploads\/2022\/06\/Andrew_wiles1-3.jpeg 1874w\" sizes=\"(max-width: 1152px) 100vw, 1152px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-f1f7639 elementor-widget elementor-widget-text-editor\" data-id=\"f1f7639\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: center;\">Andrew Wiles &#8211; Lyckades med sin barndomsdr\u00f6m att l\u00f6sa Fermats sats<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Fermats sats &#8211; Det enkla problemet med sv\u00e5r l\u00f6sning eller det finns inga positiva heltalsl\u00f6sningar som tillfredst\u00e4ller ekvationen om \u00e4r st\u00f6rre \u00e4n 2. En mycket enkel sats som de flesta kan f\u00f6rst\u00e5. Det \u00e4r en sats som Pierre de Fermat (1607-1665) formulerade 1637 i marginalen av hans exemplar av Diofantes bok Artihmetica. Fermat p\u00e5stod ocks\u00e5 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"om_disable_all_campaigns":false,"_uag_custom_page_level_css":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"site-sidebar-layout":"no-sidebar","site-content-layout":"page-builder","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"disabled","ast-breadcrumbs-content":"","ast-featured-img":"disabled","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"class_list":["post-26770","page","type-page","status-publish","hentry"],"aioseo_notices":[],"uagb_featured_image_src":{"full":false,"thumbnail":false,"medium":false,"medium_large":false,"large":false,"1536x1536":false,"2048x2048":false},"uagb_author_info":{"display_name":"joji9555@hotmail.com","author_link":"https:\/\/mahifi.se\/?author=1"},"uagb_comment_info":0,"uagb_excerpt":"Fermats sats &#8211; Det enkla problemet med sv\u00e5r l\u00f6sning eller det finns inga positiva heltalsl\u00f6sningar som tillfredst\u00e4ller ekvationen om \u00e4r st\u00f6rre \u00e4n 2. En mycket enkel sats som de flesta kan f\u00f6rst\u00e5. Det \u00e4r en sats som Pierre de Fermat (1607-1665) formulerade 1637 i marginalen av hans exemplar av Diofantes bok Artihmetica. Fermat p\u00e5stod ocks\u00e5&hellip;","_links":{"self":[{"href":"https:\/\/mahifi.se\/index.php?rest_route=\/wp\/v2\/pages\/26770","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mahifi.se\/index.php?rest_route=\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/mahifi.se\/index.php?rest_route=\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/mahifi.se\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mahifi.se\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=26770"}],"version-history":[{"count":46,"href":"https:\/\/mahifi.se\/index.php?rest_route=\/wp\/v2\/pages\/26770\/revisions"}],"predecessor-version":[{"id":28328,"href":"https:\/\/mahifi.se\/index.php?rest_route=\/wp\/v2\/pages\/26770\/revisions\/28328"}],"wp:attachment":[{"href":"https:\/\/mahifi.se\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=26770"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}