{"id":5155,"date":"2019-03-28T16:21:49","date_gmt":"2019-03-28T14:21:49","guid":{"rendered":"http:\/\/pimedios.es\/?p=5155"},"modified":"2019-03-28T16:21:49","modified_gmt":"2019-03-28T14:21:49","slug":"el-pequeno-teorema-de-fermat","status":"publish","type":"post","link":"http:\/\/pimedios.jesussoto.es\/?p=5155","title":{"rendered":"El peque\u00f1o teorema de Fermat"},"content":{"rendered":"<p>La figura de Fermat es recurrente en este blog, y su peque\u00f1o teorema ya nos sali\u00f3. Hoy daremos un poco m\u00e1s de su historia y la demostraci\u00f3n. Empecemos.<\/p>\n<p>Como dijimos Fermat enunciaba, en una carta fechada el 18 de octubre de 16 a\u00a0Fr\u00e9nicle de Bessy,\u00a0que,\u00a0<em>si a es un n\u00famero entero cualquiera y p es un n\u00famero primo que no es un factor de a, entonces p debe ser un factor del n\u00famero <\/em><span style=\"white-space: nowrap;\">$a^{p-1}-1$<\/span>. Y como era habitual en el no present\u00f3 la demostraci\u00f3n(t<em>e enviar\u00eda la demostraci\u00f3n, si no temiera que fuera demasiado larga,<\/em> le escribi\u00f3 el muy truh\u00e1n).<\/p>\n<p>La primera demostraci\u00f3n se publicar\u00eda en 1736, por Euler, aunque parece ser que Leibniz la conoc\u00eda ya en 1683.<\/p>\n<p>No conozco la demostraci\u00f3n que ofreci\u00f3 Euler(es muy probable que fuese utilizando la funci\u00f3n fi de Euler), pero s\u00ed esta que es muy sencilla.<br \/>\n<iframe loading=\"lazy\" src=\"https:\/\/www.youtube.com\/embed\/Mfbg8AYYeiI?start=3\" width=\"560\" height=\"315\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<p>&nbsp;<\/p>\n<blockquote><p>Este post forma parte del\u00a0<a href=\"https:\/\/carnavaldematematicas.wordpress.com\/\"><b>Carnaval de Matem\u00e1ticas<\/b><\/a>, que en esta octag\u00e9sima segunda edici\u00f3n, tambi\u00e9n denominada X.2, est\u00e1 organizado por\u00a0<b>Rafael Mart\u00ednez Gonz\u00e1lez<\/b>\u00a0a trav\u00e9s de su blog\u00a0<a href=\"http:\/\/elmundoderafalillo.blogspot.com.es\/\"><b>El mundo de Rafalillo<\/b><\/a>.<\/p><\/blockquote>\n","protected":false},"excerpt":{"rendered":"<p>Demostraci\u00f3n del Teorema peque\u00f1o de Fermat<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[6,9],"tags":[136,499],"class_list":["post-5155","post","type-post","status-publish","format-standard","hentry","category-historia","category-personajes","tag-fermat","tag-pequeno-teorema-de-fermat","entry"],"_links":{"self":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/5155","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5155"}],"version-history":[{"count":3,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/5155\/revisions"}],"predecessor-version":[{"id":5158,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/5155\/revisions\/5158"}],"wp:attachment":[{"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5155"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5155"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/pimedios.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5155"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}