{"id":4353,"date":"2012-06-19T13:53:15","date_gmt":"2012-06-19T12:53:15","guid":{"rendered":"http:\/\/www.walkingrandomly.com\/?p=4353"},"modified":"2012-06-21T11:17:06","modified_gmt":"2012-06-21T10:17:06","slug":"sum-of-three-cubes-puzzle","status":"publish","type":"post","link":"https:\/\/walkingrandomly.com\/?p=4353","title":{"rendered":"Sum of Three Cubes Puzzle"},"content":{"rendered":"<p>It is possible to write many integers as the sum of the cubes of three integers.\u00a0 For example<\/p>\n<p>99 = (-5)^3 + 2^3+ 6^3<\/p>\n<p>A more complicated example is<\/p>\n<p>91 = (-67134)^3 + (-65453)^3+(83538)^3<\/p>\n<p>Your task is to find integers x,y and z such that<\/p>\n<p>33 = x^3 + y^3 + z^3<\/p>\n<p>Hint: This is not a trivial problem and will (probably) require the use of a computer.  Extra credit given if you also post your source code.<\/p>\n<p><strong>Update 3: <\/strong>If you are serious about attempting to crack this problem (and some people seem to be, judging from the comments), the following reference may be of help.\u00a0 The bibliography includes other jumping off points for this problem.<\/p>\n<ul>\n<li>Michael Beck, Eric Pine, Wayne Tarrant and Kim Yarbrough Jensen: <strong>New integer representations as the sum of three cubes <\/strong>Math. Comp. <strong>76<\/strong> (2007), 1683-1690 (<a href=\"http:\/\/www.ams.org\/journals\/mcom\/2007-76-259\/S0025-5718-07-01947-3\/\">Link<\/a>)<\/li>\n<\/ul>\n<p><strong>Update 2: <\/strong>This problem is, in fact, a long-standing unsolved problem in number theory.\u00a0 If my memory serves me correctly, it is mentioned in the book <a href=\"http:\/\/www.amazon.co.uk\/gp\/product\/0387208607\/ref=as_li_ss_tl?ie=UTF8&amp;tag=walkingrandom-21&amp;linkCode=as2&amp;camp=1634&amp;creative=19450&amp;creativeASIN=0387208607\">Unsolved Problems in Number Theory<\/a><img loading=\"lazy\" decoding=\"async\" style=\"border: none !important; margin: 0px !important;\" src=\"http:\/\/www.assoc-amazon.co.uk\/e\/ir?t=walkingrandom-21&amp;l=as2&amp;o=2&amp;a=0387208607\" border=\"0\" alt=\"\" width=\"1\" height=\"1\" \/><\/p>\n<p><strong>Update 1:<\/strong> 33 is very VERY difficult so why not use 16 as a warm up problem.  MUCH smaller search space.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>It is possible to write many integers as the sum of the cubes of three integers.\u00a0 For example 99 = (-5)^3 + 2^3+ 6^3 A more complicated example is 91 = (-67134)^3 + (-65453)^3+(83538)^3 Your task is to find integers x,y and z such that 33 = x^3 + y^3 + z^3 Hint: This is [&hellip;]<\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"jetpack_post_was_ever_published":false,"footnotes":"","jetpack_publicize_message":"","jetpack_publicize_feature_enabled":true,"jetpack_social_post_already_shared":false,"jetpack_social_options":{"image_generator_settings":{"template":"highway","default_image_id":0,"font":"","enabled":false},"version":2}},"categories":[6],"tags":[],"class_list":["post-4353","post","type-post","status-publish","format-standard","hentry","category-general-math"],"jetpack_publicize_connections":[],"jetpack_featured_media_url":"","jetpack_shortlink":"https:\/\/wp.me\/p3swhs-18d","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/4353","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4353"}],"version-history":[{"count":5,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/4353\/revisions"}],"predecessor-version":[{"id":4357,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=\/wp\/v2\/posts\/4353\/revisions\/4357"}],"wp:attachment":[{"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4353"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4353"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/walkingrandomly.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4353"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}