{"id":1442,"date":"2020-01-29T09:16:12","date_gmt":"2020-01-29T14:16:12","guid":{"rendered":"http:\/\/josmfs.net\/?p=1442"},"modified":"2024-04-10T12:54:16","modified_gmt":"2024-04-10T16:54:16","slug":"quintic-nightmare","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/01\/29\/quintic-nightmare\/","title":{"rendered":"Quintic Nightmare"},"content":{"rendered":"<p><img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1440\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/01\/Quintic-Nightmare-Fig2.jpg\" alt=\"\" width=\"200\" height=\"128\" \/>Here is another challenging problem from the 2004 <em>Pi in the Sky<\/em> Canadian magazine for high school students.<\/p>\n<p>\u201c<strong>Problem 4<\/strong>. Find the real solutions of the system<br \/>\n<span style=\"color: #ffffff;\">________________<\/span> (x + y)^5 = z,<br \/>\n<span style=\"color: #ffffff;\">________________<\/span> (y + z)^5 = x,<br \/>\n<span style=\"color: #ffffff;\">________________<\/span> (z + x)^5 = y.\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Quintic-Nightmare-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See the <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/01\/Quintic-Nightmare-191021.pdf\">Quintic Nightmare<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Here is another challenging problem from the 2004 Pi in the Sky Canadian magazine for high school students. \u201cProblem 4. Find the real solutions of the system ________________ (x + y)^5 = z, ________________ (y + z)^5 = x, ________________ (z + x)^5 = y.\u201d Answer. See the Quintic Nightmare for a solution.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[3],"tags":[133,162],"class_list":["post-1442","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-algebra","tag-pi-in-the-sky"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1442","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=1442"}],"version-history":[{"count":3,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1442\/revisions"}],"predecessor-version":[{"id":3782,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1442\/revisions\/3782"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1442"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1442"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1442"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}