{"id":14869,"date":"2014-02-16T18:51:14","date_gmt":"2014-02-16T21:51:14","guid":{"rendered":"http:\/\/clubes.obmep.org.br\/blog\/?page_id=14869"},"modified":"2023-01-19T03:15:22","modified_gmt":"2023-01-19T06:15:22","slug":"algoritmo-de-euclides-para-determinacao-de-mdc-um-segundo-estudo","status":"publish","type":"page","link":"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudos-algoritmo-de-euclides-para-determinacao-de-mdc\/algoritmo-de-euclides-para-determinacao-de-mdc-um-segundo-estudo\/","title":{"rendered":"Algoritmo de Euclides para determina\u00e7\u00e3o de MDC &#8211; Um segundo estudo"},"content":{"rendered":"<p style=\"margin:10px \">\n<table style=\" height:auto; margin-left: auto; margin-right: auto;width:644px;\">\n<tr class=\"bf\">\n<td style=\"border: 1px solid #ffffff\">\n<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1001 alignright\" style=\"border: 0px;\" alt=\"\" src=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2013\/01\/menino.jpg\" width=\"95\" height=\"115\" \/><\/td>\n<td  style=\"border: 1px solid  #ffffff\">\n<p style=\"text-align: justify; border-style: dotted; border-color: #1C1C1C; border-width: thin; width: 520px; background-color: #EEE9E9; padding: 10px;\"><span style=\"color: #616161; font-family: calibri, sans-serif; font-size: 16px;\">Disponibilizamos aqui material de apoio para um segundo estudo do Algoritmo de Euclides.<br \/>\nAqui voc\u00eas ter\u00e3o que se dedicar um pouco mais aos estudos; mas vale a pena, voc\u00eas v\u00e3o aprender muito mais&#8230;<br \/>\n<strong>Bom proveito!<\/strong><\/span><\/p>\n<\/td>\n<\/tr>\n<\/table>\n<p style=\"margin:30px \">\n<div style=\"border: 8px double #CDC9C9; padding: 5px;padding-left: 20px; padding-right: 20px;\">\n<p style=\"margin:30px \">\n<div style=\"border: 2px dotted #CDC9C9; padding: 5px;padding-left: 20px; padding-right: 20px;\">\n<p style=\"margin:10px \">\n<p style=\"text-align: center;  padding-right: 15px;\"><span style=\"color: #bdb7b7; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 24px;\"><strong>I &#8211; V\u00eddeo<\/strong><\/span><\/p>\n<hr style=\"height:2px;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 30px; border: 0 none\"\/>\n<p style=\"text-align: center;\">\n<iframe loading=\"lazy\" width=\"640\" height=\"360\" src=\"https:\/\/www.youtube.com\/embed\/Ts7gyXDUm4A?rel=0\" allowfullscreen><\/iframe><br \/>\n<span style=\"font-family: calibri, sans-serif; font-size: 16px;\">\t<strong>Algoritmo de Euclides revisitado<\/strong><br \/>\nProfessor Fabio Henrique Teixeira de Souza.<\/span><\/p>\n<\/div>\n<p style=\"margin:50px \">\n<hr style=\"height:1px; width:20%;background-color:#CDC9C9; margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:40%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:3px; width:50%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:3px; width:50%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:2px; width:40%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:1px; width:20%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"margin:50px \">\n<div style=\"border: 2px dotted #CDC9C9; padding: 5px;padding-left: 20px; padding-right: 20px;\">\n<p style=\"margin:10px \">\n<p style=\"text-align: center; padding-right: 15px;\"><span style=\"color: #bdb7b7; font-family: verdana, Arial, Helvetica, sans-serif; font-size: 24px;\"><strong>II &#8211; Textos<\/strong><\/span><\/p>\n<hr style=\"height:2px;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:1px;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 20px; border: 0 none\"\/>\n<span style=\"font-family: calibri, sans-serif; font-size: 16px; color: #1c1c1c;\"><br \/>\n<span style=\"color: #CDB5CD; font-size: 20px;\"><strong>&#8226;<\/strong> <\/span><a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/02\/Aula03-MDC_MMC_Euclides.pdf\" target=\"_blank\"><span style=\"color: #1c1c1c;\"><strong>MDC, MMC, Algoritmo de Euclides e o Teorema de Bachet-B\u00e9zout <\/strong><\/span><\/a>: Carlos Gustavo Moreira.<\/p>\n<p><span style=\"color: #CDB5CD; font-size: 20px;\"><strong>&#8226;<\/strong> <\/span><a href=\"http:\/\/clubes.obmep.org.br\/blog\/wp-content\/uploads\/2014\/02\/Aula03-Algoritmo_de_Euclides_samuel.pdf\" target=\"_blank\"><span style=\"color: #1c1c1c;\"><strong>O Algoritmo de Euclides<\/strong><\/span><\/a>: Samuel Feitosa.<\/span><\/p>\n<\/div>\n<p style=\"margin:50px \">\n<hr style=\"height:1px; width:20%;background-color:#CDC9C9; margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px; width:40%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:3px; width:50%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:3px; width:50%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:2px; width:40%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:1px; width:20%;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<p style=\"margin:50px \">\n<div style=\"border: 2px dotted #CDC9C9; padding: 5px;padding-left: 20px; padding-right: 20px;\">\n<p style=\"margin:10px \">\n<p style=\"text-align: center;  padding-right: 15px;\"><span style=\"color: #bdb7b7; font-family: verdana, Arial, Helvetica, sans-serif;font-size: 24px;\"><strong>III &#8211; Alguns Problemas<\/strong><\/span><\/p>\n<hr style=\"height:2px;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 8px; border: 0 none\"\/>\n<hr style=\"height:2px;background-color:#CDC9C9;  margin-top: 8px; margin-bottom: 40px; border: 0 none\"\/>\n<p style=\"text-align: justify; border-style: solid; border-color: #CDC9C9; border-width: thin; width: 98%; padding: 10px;\"><span style=\"color: #616161; font-family: calibri, sans-serif; font-size: 17px;line-height: 25px;\"><strong>1)<\/strong> Sejam [tex]a[\/tex] e [tex]b[\/tex] n\u00fameros naturais n\u00e3o nulos.<br \/>\nMostre que:<br \/>\n[tex]\\, \\, \\, (i)\\, \\,  mdc(0,0)[\/tex] n\u00e3o est\u00e1 definido;<br \/>\n[tex]\\, \\, \\, (ii)\\, \\,  mdc(n,n) = n[\/tex], para qualquer natural n\u00e3o nulo [tex]n[\/tex];<br \/>\n[tex]\\, \\, \\, (iii)\\, \\,  mdc(m,n) = mdc(n,m)[\/tex], para quaisquer n\u00fameros naturais n\u00e3o ambos nulos [tex]m[\/tex] e [tex]n[\/tex];<br \/>\n[tex]\\, \\, \\, (iv)\\, \\,  mdc(n,0) = n[\/tex], para qualquer n\u00famero natural n\u00e3o nulo [tex]n[\/tex].<\/span><\/p>\n<p style=\"text-align: justify; border-style: solid; border-color: #CDC9C9; border-width: thin; width: 98%; padding: 10px;\"><span style=\"color: #616161; font-family: calibri, sans-serif; font-size: 17px;line-height: 25px;\"><strong>2)<\/strong> Sejam [tex]a[\/tex] e [tex]b[\/tex] n\u00fameros naturais n\u00e3o nulos, com [tex]a>b[\/tex].<br \/>\nMostre que se [tex]r[\/tex] \u00e9 o resto da divis\u00e3o de [tex]a[\/tex] por [tex]b[\/tex], ent\u00e3o  [tex]mdc(a,b)=mdc(b,r)[\/tex].<\/span><\/p>\n<\/div>\n<hr style=\"height:2px; width:100%;background-color:#CDC9C9; margin-top: 50px; margin-bottom: 8px;border: 0 none\"\/>\n<hr style=\"height:2px; width:100%;background-color:#CDC9C9; margin-top: 8px; margin-bottom: 8px;border: 0 none\"\/>\n<p style=\"text-align: right;\"><span style=\"color: #bdb7b7;\"><strong>Sonia Regina Di Giacomo<\/strong><br \/>\nEquipe COM &#8211; OBMEP<\/span><\/p>\n<\/div>\n<p style=\"text-align: right;\"><a href=\"http:\/\/clubes.obmep.org.br\/blog\/?p=7507\" title=\"Voltar\"><span style=\"color: #aca6a6;\"><strong>Voltar para a Sala de Estudos sobre o Algoritmo de Euclides<\/strong><\/span><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Disponibilizamos aqui material de apoio para um segundo estudo do Algoritmo de Euclides. Aqui voc\u00eas ter\u00e3o que se dedicar um pouco mais aos estudos; mas vale a pena, voc\u00eas v\u00e3o aprender muito mais&#8230; Bom proveito! I &#8211; V\u00eddeo Algoritmo de Euclides revisitado Professor Fabio Henrique Teixeira de Souza. II &#8211; Textos &#8226; MDC, MMC, Algoritmo &hellip; <\/p>\n<p><a class=\"more-link btn\" href=\"https:\/\/clubes.obmep.org.br\/blog\/sala-de-estudos-algoritmo-de-euclides-para-determinacao-de-mdc\/algoritmo-de-euclides-para-determinacao-de-mdc-um-segundo-estudo\/\">Continue lendo<\/a><\/p>\n","protected":false},"author":2,"featured_media":0,"parent":7507,"menu_order":5,"comment_status":"closed","ping_status":"closed","template":"template-onecolumn.php","meta":{"footnotes":""},"class_list":["post-14869","page","type-page","status-publish","hentry","nodate","item-wrap"],"_links":{"self":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/14869","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/comments?post=14869"}],"version-history":[{"count":72,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/14869\/revisions"}],"predecessor-version":[{"id":183097,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/14869\/revisions\/183097"}],"up":[{"embeddable":true,"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/pages\/7507"}],"wp:attachment":[{"href":"https:\/\/clubes.obmep.org.br\/blog\/wp-json\/wp\/v2\/media?parent=14869"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}