{"id":1996,"date":"2021-01-23T09:15:59","date_gmt":"2021-01-23T14:15:59","guid":{"rendered":"http:\/\/josmfs.net\/?p=1996"},"modified":"2021-01-23T09:15:59","modified_gmt":"2021-01-23T14:15:59","slug":"playing-with-polys","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2021\/01\/23\/playing-with-polys\/","title":{"rendered":"Playing with Polys"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft  wp-image-1994\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Playing-with-Polys-Fig2.jpg\" alt=\"\" width=\"204\" height=\"186\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Playing-with-Polys-Fig2.jpg 402w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Playing-with-Polys-Fig2-300x274.jpg 300w\" sizes=\"auto, (max-width: 204px) 100vw, 204px\" \/>Here is a fairly straight-forward problem from <em>500 Mathematical Challenges<\/em>.<\/p>\n<p><strong>\u201cProblem 256.<\/strong>\u00a0 Let <em>n<\/em> be a positive integer. Show that (<em>x<\/em> \u2013 1)<sup>2<\/sup> is a factor of <em>x<sup>n<\/sup> \u2013 n<\/em>(<em>x<\/em> \u2013 1) \u2013 1.\u201d<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2021\/01\/Playing-with-Polys-201107.pdf\">Playing with Polys<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is a fairly straight-forward problem from 500 Mathematical Challenges. \u201cProblem 256.\u00a0 Let n be a positive integer. Show that (x \u2013 1)2 is a factor of xn \u2013 n(x \u2013 1) \u2013 1.\u201d See Playing with Polys<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[177,133],"class_list":["post-1996","post","type-post","status-publish","format-standard","hentry","category-math-inquiries","tag-500-math-challenges","tag-algebra"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1996","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/comments?post=1996"}],"version-history":[{"count":1,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1996\/revisions"}],"predecessor-version":[{"id":1997,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1996\/revisions\/1997"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}