{"id":791,"date":"2018-09-23T07:04:08","date_gmt":"2018-09-23T07:04:08","guid":{"rendered":"https:\/\/blogs.ua.es\/dimates\/?p=791"},"modified":"2018-09-30T07:28:46","modified_gmt":"2018-09-30T07:28:46","slug":"los-polinomios-del-2017-y-del-2018","status":"publish","type":"post","link":"https:\/\/blogs.ua.es\/dimates\/2018\/09\/23\/los-polinomios-del-2017-y-del-2018\/","title":{"rendered":"Los Polinomios del 2017 y del 2018"},"content":{"rendered":"<pre>Problema 7 de la Olitele (Olimpiada Telem\u00e1tica de Catalu\u00f1a) 2017\r\nSe dirige a una edad de: 16-17 a\u00f1os<\/pre>\n<p>a) Para una funci\u00f3n polin\u00f3mica de segundo grado p(x) = x\u00b2 + ax + b con coeficientes a y b enteros, existen dos n\u00fameros diferentes m y n que cumplen p(m) = p(n) = 2017. Demuestra que no existe ning\u00fan n\u00famero entero z que cumpla p(z) = 2018.<\/p>\n<p>b) Dar un ejemplo de una funci\u00f3n polin\u00f3mica q(x) con coeficientes enteros para la cual existan tres n\u00fameros enteros n, m y z que cumplan q(m) = q(n) = 2017 y q(z) = 2018.<\/p>\n<p>c) Para una funci\u00f3n polin\u00f3mica de grado n f(x) = x<sup>n<\/sup> + \u2026 con coeficientes enteros, existen tres n\u00fameros enteros diferentes m, q y r, que cumplen f(m) = f(q) = f(r) = 2017. Demuestra que no puede haber ning\u00fan n\u00famero entero z que cumpla f(z) = 2018.<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"aligncenter size-full wp-image-792\" src=\"https:\/\/blogs.ua.es\/dimates\/files\/2018\/09\/33.Polinomios20172018.png\" alt=\"\" width=\"300\" height=\"300\" srcset=\"https:\/\/blogs.ua.es\/dimates\/files\/2018\/09\/33.Polinomios20172018.png 300w, https:\/\/blogs.ua.es\/dimates\/files\/2018\/09\/33.Polinomios20172018-150x150.png 150w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><br \/>\nSoluci\u00f3n: <a href=\"https:\/\/blogs.ua.es\/dimates\/2018\/09\/29\/solucion-a-los-polinomios-del-2017-y-del-2018\/\">Aqu\u00ed<\/a>.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Problema 7 de la Olitele (Olimpiada Telem\u00e1tica de Catalu\u00f1a) 2017 Se dirige a una edad de: 16-17 a\u00f1os a) Para una funci\u00f3n polin\u00f3mica de segundo grado p(x) = x\u00b2 + ax + b con coeficientes a y b enteros, existen dos n\u00fameros diferentes m y n que cumplen p(m) = p(n) = 2017. Demuestra que [&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-791","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\/791","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=791"}],"version-history":[{"count":4,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/791\/revisions"}],"predecessor-version":[{"id":822,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/posts\/791\/revisions\/822"}],"wp:attachment":[{"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/media?parent=791"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/categories?post=791"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/blogs.ua.es\/dimates\/wp-json\/wp\/v2\/tags?post=791"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}