{"id":214,"date":"2018-02-20T10:45:32","date_gmt":"2018-02-20T09:45:32","guid":{"rendered":"http:\/\/clases.jesussoto.es\/?p=214"},"modified":"2018-02-20T09:26:06","modified_gmt":"2018-02-20T08:26:06","slug":"mad-divisibilidad","status":"publish","type":"post","link":"https:\/\/curso17.jesussoto.es\/?p=214","title":{"rendered":"MAD: Divisibilidad"},"content":{"rendered":"<p>El concepto de divisibilidad es uno de los m\u00e1s importantes que veremos en Teor\u00eda de n\u00fameros. Con \u00e9l pretendemos dar una sustituci\u00f3n de la divisi\u00f3n que no siempre es posible en el conjunto de los n\u00fameros enteros.<\/p>\n<p>Decimos que un n\u00famero entero $b$ es divisible entre un entero $a$ (distinto de cero) si existe un entero $c$ tal que: $$b = a \u00b7 c.$$<br \/>\nSe suele expresar de la forma $a|b$, que se lee: $a$ divide a $b$, o $a$ es un divisor de $b$, o, tambi\u00e9n $b$ es m\u00faltiplo de $a$.<\/p>\n<p>Utilizando esta definici\u00f3n hemos probado propiedades de la divisibilidad como<\/p>\n<ul>\n<li>$1|a$  y $a|0$ para todo $x\\in\\mathbb{Z}$.<\/li>\n<li>Si $a|b$, entonces $|a|&lt;|b|$.<\/li>\n<li>Si $a|b$ y $b|a$, entonces $a=\\pm b$.<\/li>\n<li>Si $a|b$, entonces $a|(bx)$ para todo $x\\in\\mathbb{Z}$.<\/li>\n<li>Si $a|b$ y $b|c$, entonces $a|c$.<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<table id=\"yzpi\" width=\"100%\" border=\"0\" cellspacing=\"0\" cellpadding=\"3\" bgcolor=\"#999999\">\n<tbody>\n<tr>\n<td width=\"100%\"><strong>Ejercicio:<\/strong> Probar que si $a|b$ y $a|c$, entonces $a|(bx+cy)$, para todo $x,y\\in\\mathbb{Z}$<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>El concepto de divisibilidad es uno de los m\u00e1s importantes que veremos en Teor\u00eda de n\u00fameros. Con \u00e9l pretendemos dar una sustituci\u00f3n de la divisi\u00f3n que no siempre es posible en el conjunto de los n\u00fameros enteros. Decimos que un n\u00famero entero $b$ es divisible entre un entero $a$ (distinto de cero) si existe un&hellip; <a class=\"more-link\" href=\"https:\/\/curso17.jesussoto.es\/?p=214\">Seguir leyendo <span class=\"screen-reader-text\">MAD: Divisibilidad<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":[],"categories":[5],"tags":[],"_links":{"self":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/214"}],"collection":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=214"}],"version-history":[{"count":2,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/214\/revisions"}],"predecessor-version":[{"id":216,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=\/wp\/v2\/posts\/214\/revisions\/216"}],"wp:attachment":[{"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=214"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=214"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/curso17.jesussoto.es\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=214"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}