{"id":6827,"date":"2019-03-13T10:29:39","date_gmt":"2019-03-13T14:29:39","guid":{"rendered":"https:\/\/library.bc.edu\/answerwall\/?p=6827"},"modified":"2019-03-13T16:27:23","modified_gmt":"2019-03-13T20:27:23","slug":"why-x2-2-2y23-never-an-integer-for-xy%e2%88%88z","status":"publish","type":"post","link":"https:\/\/library.bc.edu\/answerwall\/2019\/03\/13\/why-x2-2-2y23-never-an-integer-for-xy%e2%88%88z\/","title":{"rendered":"Why x^2-2\/2y^2+3 never an integer for x,y,\u2208z"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"318\" height=\"320\" src=\"https:\/\/library.bc.edu\/answerwall\/wp-content\/uploads\/2019\/03\/aw031319-2.jpg\" alt=\"Why x^2-2\/2y^2+3 never an integer for x,y,\u2208Z\" class=\"wp-image-6825\" srcset=\"https:\/\/library.bc.edu\/answerwall\/wp-content\/uploads\/2019\/03\/aw031319-2.jpg 318w, https:\/\/library.bc.edu\/answerwall\/wp-content\/uploads\/2019\/03\/aw031319-2-150x150.jpg 150w, https:\/\/library.bc.edu\/answerwall\/wp-content\/uploads\/2019\/03\/aw031319-2-298x300.jpg 298w, https:\/\/library.bc.edu\/answerwall\/wp-content\/uploads\/2019\/03\/aw031319-2-100x100.jpg 100w\" sizes=\"auto, (max-width: 318px) 100vw, 318px\" \/><figcaption>Why x^2-2\/2y^2+3 never an integer for x,y,\u2208Z<\/figcaption><\/figure>\n\n\n\n<p>(x^2 \u2212 2)\/(2y^2 + 3) can be shown never to be an integer, when x and y are integers, using a proof by contradiction. See question 5 of this problem set for the full solution (<a href=\"http:\/\/bit.ly\/contradictionproof\">bit.ly\/contradictionproof<\/a>).<\/p>\n","protected":false},"excerpt":{"rendered":"<p>(x^2 \u2212 2)\/(2y^2 + 3) can be shown never to be an integer, when x and y are integers, using a proof by contradiction. See question 5 of this problem set for the full solution (bit.ly\/contradictionproof).<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12],"tags":[99],"class_list":["post-6827","post","type-post","status-publish","format-standard","hentry","category-academics","tag-mathematics"],"_links":{"self":[{"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/posts\/6827","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/comments?post=6827"}],"version-history":[{"count":3,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/posts\/6827\/revisions"}],"predecessor-version":[{"id":6839,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/posts\/6827\/revisions\/6839"}],"wp:attachment":[{"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/media?parent=6827"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/categories?post=6827"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/tags?post=6827"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}