{"id":25339,"date":"2025-09-11T23:16:43","date_gmt":"2025-09-11T20:16:43","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=25339"},"modified":"2025-10-22T19:16:02","modified_gmt":"2025-10-22T16:16:02","slug":"problem-of-the-month-september-2025","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-september-2025\/","title":{"rendered":"Problem of the Month \u2013 September 2025"},"content":{"rendered":"<p>Find all pairs (<em>p, n<\/em>), where <em>p<\/em> is a prime number and <em>n &lt; p<\/em> is a positive integer number such that <em>pn<\/em>(<em>p<\/em> + 1)(<em>n<\/em> + 1) + 1 is a perfect square.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>\u00c7a\u011fr\u0131 Mara\u015fl\u0131 Ankara \u00d6zel Y\u0131ld\u0131z S\u0131nav Ortaokulu<\/li>\n<li>Vedat Deveci \u0130stanbul<\/li>\n<li>Albert Stadler Herrliberg, Switzerland<\/li>\n<li>Tamer T\u00fcrko\u011flu<\/li>\n<li>O\u011fuz \u00c7etin Bursa<\/li>\n<li>Hari Kishan D.N. College Meerut, India<\/li>\n<li>As\u0131m Ka\u011fan O\u011fuz Bilkent University<\/li>\n<li>Recep Bindak Gaziantep<\/li>\n<li>Halil \u0130brahim Dokuyucu T\u0130SK\u0130, Trabzon<\/li>\n<li>Mustafa Kaynak Gaziantep<\/li>\n<li>Ahmet Erhan Avc\u0131 Bilkent University<\/li>\n<li>Cuma G\u00fcng\u00f6r\u00fc<\/li>\n<li>Abdulkadir Tanr\u0131verdi Eski\u015fehir<\/li>\n<li>Ahmet Yasir Bora Istanbul Technical University<\/li>\n<li>Soyunmuhammet Geldimammedov School 49, Ashgabat, Turkmenistan<\/li>\n<li>Yavuz Selim \u0130pek \u0130zmir Dokuz Eyl\u00fcl University<\/li>\n<li>Levent Ko\u00e7alan \u0130zmir<\/li>\n<li>Begench Akmyradov Ashgabat, Turkmenistan<\/li>\n<li>Murat Be\u015fli Politecnico di Torino, Italy<\/li>\n<li>Ahmet Y\u00fcksel Ayd\u0131n<\/li>\n<li>Khaled Halaoua Higher Institute of Appl. Sci. and Tech., Damascus, Syria<\/li>\n<li>Muhammed Y\u00fcksel Hacettepe University<\/li>\n<li>J\u00fcrgen Weith University of Appl. Sci. W\u00fcrzburg-Schweinfurt, Germany<\/li>\n<li>Magnus Jakobsson Lund, Sweden<\/li>\n<li>Mehmet Sarak Bilkent University<\/li>\n<li>Roger Bengtsson Lund, Sweden<\/li>\n<li>Eray Ege Tokg\u00f6z Bilkent University<\/li>\n<li>Javad Aliyev Middle East Technical University<\/li>\n<li>\u00d6zg\u00fcr Soysal<\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<a href=\"https:\/\/math.bilkent.edu.tr\/Problem\/2509a.pdf\">https:\/\/math.bilkent.edu.tr\/Problem\/2509a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Find all pairs (p, n), where p is a prime number and n &lt; p is a positive integer number such that pn(p + 1)(n + 1) + 1 is a perfect square. &nbsp; Correct Solutions by, Toshihiro Shimizu Kawasaki, Japan \u00c7a\u011fr\u0131 Mara\u015fl\u0131 Ankara \u00d6zel Y\u0131ld\u0131z S\u0131nav Ortaokulu Vedat Deveci [\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-september-2025\/\" 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-25339","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25339","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=25339"}],"version-history":[{"count":4,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25339\/revisions"}],"predecessor-version":[{"id":25711,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25339\/revisions\/25711"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=25339"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}