{"id":25056,"date":"2025-07-08T13:12:30","date_gmt":"2025-07-08T10:12:30","guid":{"rendered":"https:\/\/w3.bilkent.edu.tr\/en\/?page_id=25056"},"modified":"2025-09-11T23:20:30","modified_gmt":"2025-09-11T20:20:30","slug":"problem-of-the-month-july-august-2025","status":"publish","type":"page","link":"https:\/\/w3.bilkent.edu.tr\/en\/problem-of-the-month-july-august-2025\/","title":{"rendered":"Problem of the Month \u2013 July, August 2025"},"content":{"rendered":"<p>Let <em>a, b, c<\/em> be pairwise relatively prime positive integers satisfying <em>a &gt; bc<\/em>. For any two positive integers <em>m &lt; n<\/em> we say that m is a successor of <em>n<\/em>, if for every pile of stones with weights <em>a, b, c<\/em> and total weight <em>n<\/em>, it is possible to remove some stones and obtain a new pile with total weight <em>m<\/em>. Find the greatest positive integer that does not have any successor.<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Correct Solutions by,<\/strong><\/p>\n<ul>\n<li>Toshihiro Shimizu Kawasaki, Japan<\/li>\n<li>Ahmet Y\u00fcksel Ayd\u0131n<\/li>\n<li>Umut Eren Bilgi\u00e7\u00a0New Albany High School, Ohio, USA<\/li>\n<li>Mert Emir<\/li>\n<li>Magnus Jakobsson Lund, Sweden<\/li>\n<li>Albert Stadler\u00a0Herrliberg, Switzerland<\/li>\n<li>Serkan Sonel\u00a0Bilkent University<\/li>\n<li>Roger Bengtsson\u00a0Lund, Sweden<\/li>\n<li>Choi Min Kyu\u00a0South Korea<\/li>\n<\/ul>\n<p><strong>Solution:\u00a0<a href=\"https:\/\/math.bilkent.edu.tr\/Problem\/2508a.pdf\">https:\/\/math.bilkent.edu.tr\/Problem\/2508a.pdf<\/a><\/strong><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Let a, b, c be pairwise relatively prime positive integers satisfying a &gt; bc. For any two positive integers m &lt; n we say that m is a successor of n, if for every pile of stones with weights a, b, c and total weight n, it is possible to [\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-july-august-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-25056","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25056","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=25056"}],"version-history":[{"count":4,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25056\/revisions"}],"predecessor-version":[{"id":25343,"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/pages\/25056\/revisions\/25343"}],"wp:attachment":[{"href":"https:\/\/w3.bilkent.edu.tr\/en\/wp-json\/wp\/v2\/media?parent=25056"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}