{"id":1637,"date":"2020-06-14T08:35:58","date_gmt":"2020-06-14T12:35:58","guid":{"rendered":"http:\/\/josmfs.net\/?p=1637"},"modified":"2024-04-08T18:59:33","modified_gmt":"2024-04-08T22:59:33","slug":"amazing-radical-sum","status":"publish","type":"post","link":"https:\/\/josmfs.net\/wordpress\/2020\/06\/14\/amazing-radical-sum\/","title":{"rendered":"Amazing Radical Sum"},"content":{"rendered":"<p><strong> <img loading=\"lazy\" decoding=\"async\" class=\"alignleft size-full wp-image-1634\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/06\/Amazing-Radical-Fig4.jpg\" alt=\"\" width=\"201\" height=\"105\" \/><\/strong>The craziness of manipulating radicals strikes again.\u00a0 This 2006 four-star problem from Colin Hughes at <em>Maths Challenge<\/em> is really astonishing, though it takes the right key to unlock it.<\/p>\n<p><strong>\u201cProblem <\/strong>Consider the following sequence:<img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1636 aligncenter\" src=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/06\/Amazing-Radical-Sum.jpg\" alt=\"\" width=\"462\" height=\"55\" srcset=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/06\/Amazing-Radical-Sum.jpg 770w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/06\/Amazing-Radical-Sum-300x36.jpg 300w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/06\/Amazing-Radical-Sum-768x92.jpg 768w, https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/06\/Amazing-Radical-Sum-624x75.jpg 624w\" sizes=\"auto, (max-width: 462px) 100vw, 462px\" \/><\/p>\n<p>For which values of [positive integer] <em>n <\/em>is S(<em>n<\/em>) rational?\u201d<\/p>\n<p><a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2024\/04\/Amazing-Radical-Sum-Answer.jpg\">Answer<\/a>.<\/p>\n<p>See <a href=\"https:\/\/josmfs.net\/wordpress\/wp-content\/uploads\/2020\/06\/Amazing-Radical-Sum-190804.pdf\">Amazing Radical Sum<\/a> for a solution.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The craziness of manipulating radicals strikes again.\u00a0 This 2006 four-star problem from Colin Hughes at Maths Challenge is really astonishing, though it takes the right key to unlock it. \u201cProblem Consider the following sequence: For which values of [positive integer] n is S(n) rational?\u201d Answer. See Amazing Radical Sum 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":[133,151,230],"class_list":["post-1637","post","type-post","status-publish","format-standard","hentry","category-puzzles-and-problems","tag-algebra","tag-colin-hughes","tag-sequences-and-series"],"_links":{"self":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1637","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=1637"}],"version-history":[{"count":4,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1637\/revisions"}],"predecessor-version":[{"id":3748,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/posts\/1637\/revisions\/3748"}],"wp:attachment":[{"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/media?parent=1637"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/categories?post=1637"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/josmfs.net\/wordpress\/wp-json\/wp\/v2\/tags?post=1637"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}