{"id":204,"date":"2020-03-25T22:50:36","date_gmt":"2020-03-26T01:50:36","guid":{"rendered":"http:\/\/cinoto.com.br\/matematica\/?p=204"},"modified":"2020-03-25T22:50:36","modified_gmt":"2020-03-26T01:50:36","slug":"qual-o-numero-de-divisores-positivos-do-numero-n9155-91410-91310-91%c2%b25-911","status":"publish","type":"post","link":"http:\/\/cinoto.com.br\/matematica\/qual-o-numero-de-divisores-positivos-do-numero-n9155-91410-91310-91%c2%b25-911\/","title":{"rendered":"2) Qual o n\u00famero de divisores positivos do n\u00famero N = 91^5 + 5.91^4 + 10.91^3 + 10.91\u00b2 + 5.91 + 1?"},"content":{"rendered":"\n<!--more-->\n\n\n\n<h2 class=\"wp-block-heading\">Resolu\u00e7\u00e3o:<\/h2>\n\n\n\n<p>Nessa aqui voc\u00ea poderia saber que:<\/p>\n\n\n\n<p>(a + b)<sup>5<\/sup>&nbsp;= a<sup>5<\/sup>&nbsp;+ 5a<sup>4<\/sup>b + 10a<sup>3<\/sup>b<sup>2<\/sup>&nbsp;+ 10 a<sup>2<\/sup>b<sup>3<\/sup>&nbsp;+&nbsp;5ab<sup>4<\/sup>&nbsp;+ b<sup>5<\/sup><\/p>\n\n\n\n<p>E a\u00ed voc\u00ea veria que se a = 91 e b = 1 teremos:<\/p>\n\n\n\n<p>(91 + 1)<sup>5<\/sup>&nbsp;= 91<sup>5<\/sup>&nbsp;+ 5.91<sup>4<\/sup>.1 + 10.91<sup>3<\/sup>.1<sup>2<\/sup>&nbsp;+ 10.91<sup>2<\/sup>.1<sup>3&nbsp;<\/sup>+ 5.91.1<sup>4<\/sup>&nbsp;+ 1<sup>5<\/sup><\/p>\n\n\n\n<p>(91 + 1)<sup>5<\/sup>&nbsp;= N<\/p>\n\n\n\n<p>Ent\u00e3o queremos saber dos divisores positivos de:<\/p>\n\n\n\n<p>N = 92<sup>5<\/sup><\/p>\n\n\n\n<p>N = (2<sup>2<\/sup>.23)<sup>5<\/sup><\/p>\n\n\n\n<p>N = (2<sup>10<\/sup>).(23<sup>5<\/sup>)<\/p>\n\n\n\n<p>E a\u00ed usamos o teorema do n\u00famero de divisores, que diz&nbsp;que o n\u00famero de divisores \u00e9 o produto dos sucessores&nbsp;dos expoentes dos fatores primos do n\u00famero:<\/p>\n\n\n\n<p>n\u00famero de divisores = (10 + 1).(5 + 1)<\/p>\n\n\n\n<p>n\u00famero de divisores = 66<\/p>\n\n\n\n<p>Alternativa c) 66<\/p>\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[5],"tags":[30],"class_list":["post-204","post","type-post","status-publish","format-standard","hentry","category-analise-combinatoria","tag-insano"],"_links":{"self":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/204","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/comments?post=204"}],"version-history":[{"count":1,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/204\/revisions"}],"predecessor-version":[{"id":205,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/posts\/204\/revisions\/205"}],"wp:attachment":[{"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/media?parent=204"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/categories?post=204"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/cinoto.com.br\/matematica\/wp-json\/wp\/v2\/tags?post=204"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}