{"id":3216,"date":"2024-03-09T18:57:49","date_gmt":"2024-03-09T18:57:49","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=3216"},"modified":"2024-03-16T19:49:38","modified_gmt":"2024-03-16T19:49:38","slug":"demasiados-cuadrados","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2024\/03\/09\/demasiados-cuadrados\/","title":{"rendered":"Demasiados cuadrados"},"content":{"rendered":"<pre>Problema 6 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2024 (viernes)\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Sean a, b, c tres n\u00fameros enteros, y sea p &gt;= 5 un n\u00famero primo.<\/p>\n<p>Demostrar que, si an\u00b2 + bn + c es el cuadrado de un n\u00famero entero para 2p \u2013 1 valores consecutivos de n, entonces b\u00b2 \u2013 4ac es un m\u00faltiplo de p.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2024\/03\/340.cuadrados.png\" alt=\"\" width=\"300\" height=\"300\" class=\"alignnone size-full wp-image-3217\" \/><\/p>\n<p>Soluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2024\/03\/16\/solucion-a-demasiados-cuadrados\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 6 de la Fase Local de la Olimpiada Espa\u00f1ola de Matem\u00e1ticas 2024 (viernes) Se dirige a una edad de: 16-17 a\u00f1os Sean a, b, c tres n\u00fameros enteros, y sea p &gt;= 5 un n\u00famero primo. Demostrar que, si an\u00b2 + bn + c es el cuadrado de un n\u00famero entero para 2p \u2013 [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2242021,1738,2242029,2849],"tags":[],"class_list":["post-3216","post","type-post","status-publish","format-standard","hentry","category-olimpiada-matematica-espanola","category-olimpiadas","category-ome","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3216","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=3216"}],"version-history":[{"count":2,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3216\/revisions"}],"predecessor-version":[{"id":3225,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3216\/revisions\/3225"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=3216"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=3216"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=3216"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}