{"id":3048,"date":"2023-10-07T17:14:09","date_gmt":"2023-10-07T17:14:09","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=3048"},"modified":"2023-10-14T12:10:07","modified_gmt":"2023-10-14T12:10:07","slug":"producto-de-factoriales","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2023\/10\/07\/producto-de-factoriales\/","title":{"rendered":"Producto de factoriales"},"content":{"rendered":"<pre>Problema 4 del concurso Olitele 2022\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>Antes de probar con este problema, deber\u00edamos saber que el factorial de un n\u00famero natural n, que se escribe n!, es n! = 1\u00b72\u00b73\u00b7\u2026\u00b7(n \u2013 1)\u00b7n.<\/p>\n<p>Consideremos el n\u00famero P, que se consigue de la siguiente manera: P = 1!\u00b72!\u00b73!\u00b7\u2026\u00b798!\u00b799!\u00b7100! (es decir, como el producto del factorial de los 100 primeros n\u00fameros).<\/p>\n<p>\u00bfCu\u00e1l es el valor del n\u00famero natural s para el cual Q = P\/(s!) es un cuadrado perfecto de un n\u00famero natural?<br \/>\n<img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2023\/10\/319.factoriales.png\" alt=\"\" width=\"300\" height=\"300\" class=\"alignnone size-full wp-image-3049\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2023\/10\/319.factoriales.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2023\/10\/319.factoriales-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2023\/10\/14\/solucion-a-producto-de-factoriales\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 4 del concurso Olitele 2022 Se dirige a una edad de: 16-17 a\u00f1os Antes de probar con este problema, deber\u00edamos saber que el factorial de un n\u00famero natural n, que se escribe n!, es n! = 1\u00b72\u00b73\u00b7\u2026\u00b7(n \u2013 1)\u00b7n. Consideremos el n\u00famero P, que se consigue de la siguiente manera: P = 1!\u00b72!\u00b73!\u00b7\u2026\u00b798!\u00b799!\u00b7100! (es [&hellip;]<\/p>\n","protected":false},"author":4267,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1738,2242014,2849],"tags":[],"class_list":["post-3048","post","type-post","status-publish","format-standard","hentry","category-olimpiadas","category-olitele","category-problemas"],"_links":{"self":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3048","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=3048"}],"version-history":[{"count":3,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3048\/revisions"}],"predecessor-version":[{"id":3058,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/3048\/revisions\/3058"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=3048"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=3048"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=3048"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}