{"id":7765,"date":"2019-04-10T10:55:08","date_gmt":"2019-04-10T14:55:08","guid":{"rendered":"https:\/\/library.bc.edu\/answerwall\/?p=7765"},"modified":"2019-04-10T16:30:02","modified_gmt":"2019-04-10T20:30:02","slug":"why-does-equation-have-four-solutions-equation-where-p-8k-1","status":"publish","type":"post","link":"https:\/\/library.bc.edu\/answerwall\/2019\/04\/10\/why-does-equation-have-four-solutions-equation-where-p-8k-1\/","title":{"rendered":"Why does [equation] have four solutions [equation] where p = 8k + 1?"},"content":{"rendered":"\n<figure class=\"wp-block-image\"><img loading=\"lazy\" decoding=\"async\" width=\"300\" height=\"295\" src=\"https:\/\/library.bc.edu\/answerwall\/wp-content\/uploads\/2019\/04\/aw041019-9.jpg\" alt=\"Why does (equation) have 4 solutions (equation) where p = 8k + 1\" class=\"wp-image-7747\"\/><figcaption>Why does (equation) have 4 solutions (equation) where p = 8k + 1<\/figcaption><\/figure>\n\n\n\n<p>\nThe Answer Wall hasn&#8217;t studied number theory or quadratic reciprocity, so I can&#8217;t help you find the solutions for this system of congruences.  If you are interested in finding the solutions, I recommend you take MATH4430 Introduction to Number Theory or speak to Professor Robert Gross who teaches that course (http:\/\/bit.ly\/RobertGross). Alternatively, you could speak to any of our Math department faculty who specialise in Number Theory &#8211; Avner Ash, Solomon Friederg, Robert Gross, Benjamin Howard, Dube Kelmer, or Keerthi Madapusi Pera (http:\/\/bit.ly\/numtheoryresearch). Good luck!\n\n<\/p>\n","protected":false},"excerpt":{"rendered":"<p>The Answer Wall hasn&#8217;t studied number theory or quadratic reciprocity, so I can&#8217;t help you find the solutions for this system of congruences. If you are interested in finding the solutions, I recommend you take MATH4430 Introduction to Number Theory or speak to Professor Robert Gross who teaches that course (http:\/\/bit.ly\/RobertGross). Alternatively, you could speak &hellip; <\/p>\n<p class=\"link-more\"><a href=\"https:\/\/library.bc.edu\/answerwall\/2019\/04\/10\/why-does-equation-have-four-solutions-equation-where-p-8k-1\/\" class=\"more-link\">Continue reading<span class=\"screen-reader-text\"> &#8220;Why does [equation] have four solutions [equation] where p = 8k + 1?&#8221;<\/span><\/a><\/p>\n","protected":false},"author":3,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-7765","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/posts\/7765","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=7765"}],"version-history":[{"count":3,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/posts\/7765\/revisions"}],"predecessor-version":[{"id":7779,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/posts\/7765\/revisions\/7779"}],"wp:attachment":[{"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/media?parent=7765"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/categories?post=7765"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/library.bc.edu\/answerwall\/wp-json\/wp\/v2\/tags?post=7765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}