{"id":17164,"date":"2022-04-07T09:39:27","date_gmt":"2022-04-07T06:39:27","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=17164"},"modified":"2022-05-09T15:51:18","modified_gmt":"2022-05-09T12:51:18","slug":"problem-of-the-month-april-2022","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-april-2022\/","title":{"rendered":"Problem of the Month \u2013 April 2022"},"content":{"rendered":"<p>For a polynomial <em>Q<\/em> with integer coefficient and prime <em>p<\/em>, we say that <em>Q<\/em> excludes <em>p<\/em> if there<br \/>\nis no integer n for which <em>p<\/em> | <em>Q<\/em>(<em>n<\/em>). Does there exists a polynomial with integer coefficients<br \/>\nhaving no rational roots which excludes exactly one prime?<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japonya<\/li>\n<li>Mustafa Burak Topal, Bo\u011fazi\u00e7i \u00dcniversitesi<\/li>\n<li>Deniz Can Kara\u00e7elebi, \u00c7i\u00e7eklik\u00f6y 50. Y\u0131l Fen ve Teknoloji Lisesi<\/li>\n<li>\u015eevket Onur Yilmaz, Kabata\u015f Erkek Lisesi<\/li>\n<li>Lujain Qazmanny, \u00dcrd\u00fcn<\/li>\n<li>Roger Bengtsson Lund, \u0130sve\u00e7<\/li>\n<\/ul>\n<p>&nbsp;<\/p>\n<p><strong>\u00c7\u00f6z\u00fcm\u00fc:\u00a0<a href=\"http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2204a.pdf\">http:\/\/www.fen.bilkent.edu.tr\/~cvmath\/Problem\/2204a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>For a polynomial Q with integer coefficient and prime p, we say that Q excludes p if there is no integer n for which p | Q(n). Does there exists a polynomial with integer coefficients having no rational roots which excludes exactly one prime? &nbsp; Correct Solutions by, Toshihiro Shimizu [\u2026] <\/p>\n<div class=\"clear\"><\/div>\n<p><a class=\"more_link clearfix\" href=\"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-april-2022\/\" rel=\"nofollow\">Read More<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-17164","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/17164","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/comments?post=17164"}],"version-history":[{"count":5,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/17164\/revisions"}],"predecessor-version":[{"id":17383,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/17164\/revisions\/17383"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=17164"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}