{"id":1862,"date":"2020-12-13T19:44:12","date_gmt":"2020-12-13T19:44:12","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=1862"},"modified":"2020-12-19T09:24:43","modified_gmt":"2020-12-19T09:24:43","slug":"numero-de-divisores","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2020\/12\/13\/numero-de-divisores\/","title":{"rendered":"N\u00famero de divisores"},"content":{"rendered":"<pre>Problema 15 del concurso marat\u00f3 de problemes 2019\r\nSe dirige a una edad de: 14-15 a\u00f1os<\/pre>\n<p>Consideramos el conjunto A<sub>n<\/sub> = {1, 2, 3, \u2026 , 10<sup>n \u2013 1<\/sup>, 10<sup>n<\/sup>} de todos los enteros positivos desde el 1 hasta el 10<sup>n<\/sup>.<\/p>\n<p>a) Razona cu\u00e1ntos n\u00fameros del conjunto A<sub>n<\/sub> son m\u00faltiplos de 2 o m\u00faltiplos de 3.<\/p>\n<p>b) Razona cu\u00e1ntos n\u00fameros del conjunto A<sub>n<\/sub> son m\u00faltiplos de 8 o m\u00faltiplos de 11.<\/p>\n<p>Nota. La o no es exclusiva, es decir, que hay que incluir en el recuento los que sean m\u00faltiplos de ambos n\u00fameros. Naturalmente, la respuesta se dar\u00e1 en funci\u00f3n de n, aunque es posible que algunos casos se deban detallar.<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2020\/12\/173.Numerodedivisores.png\" alt=\"\" width=\"300\" height=\"300\" class=\"aligncenter size-full wp-image-1863\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2020\/12\/173.Numerodedivisores.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2020\/12\/173.Numerodedivisores-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2020\/12\/19\/solucion-a-numero-de-divisores\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 15 del concurso marat\u00f3 de problemes 2019 Se dirige a una edad de: 14-15 a\u00f1os Consideramos el conjunto An = {1, 2, 3, \u2026 , 10n \u2013 1, 10n} de todos los enteros positivos desde el 1 hasta el 10n. a) Razona cu\u00e1ntos n\u00fameros del conjunto An son m\u00faltiplos de 2 o m\u00faltiplos de [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242026,1738,2849],"tags":[],"class_list":["post-1862","post","type-post","status-publish","format-standard","hentry","category-marato-de-problemes","category-olimpiadas","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/1862","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/users\/4267"}],"replies":[{"embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/comments?post=1862"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/1862\/revisions"}],"predecessor-version":[{"id":1868,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/1862\/revisions\/1868"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=1862"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=1862"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=1862"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}