{"id":35,"date":"2010-07-12T13:31:53","date_gmt":"2010-07-12T13:31:53","guid":{"rendered":"http:\/\/mathriddles.williams.edu\/?p=35"},"modified":"2025-01-27T09:41:32","modified_gmt":"2025-01-27T14:41:32","slug":"year-today-gone-tomorrow","status":"publish","type":"post","link":"https:\/\/sites.williams.edu\/mathriddles\/difficulty\/hard\/year-today-gone-tomorrow\/","title":{"rendered":"Year Today, Gone Tomorrow?"},"content":{"rendered":"<p>Consider the set {1,11,111, &#8230;, ((10^2007) &#8211; 1)\/9}.<\/p>\n<p>Prove at least one of these numbers is divisible by 2007.<\/p>\n<p>Is the same true for 2008 (replacing 10^2007 with 10^2008, of course)?<\/p>\n<p>Communicated by Michael Varnava.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Consider the set {1,11,111, &#8230;, ((10^2007) &#8211; 1)\/9}. Prove at least one of these numbers is divisible by 2007. Is the same true for 2008 (replacing 10^2007 with 10^2008, of course)? Communicated by Michael Varnava.<\/p>\n","protected":false},"author":2861,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[6,18],"tags":[],"class_list":["post-35","post","type-post","status-publish","format-standard","hentry","category-hard","category-number-theory"],"acf":[],"_links":{"self":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/35","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/users\/2861"}],"replies":[{"embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/comments?post=35"}],"version-history":[{"count":1,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/35\/revisions"}],"predecessor-version":[{"id":1194,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/posts\/35\/revisions\/1194"}],"wp:attachment":[{"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/media?parent=35"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/categories?post=35"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sites.williams.edu\/mathriddles\/wp-json\/wp\/v2\/tags?post=35"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}