{"id":570,"date":"2025-02-24T04:03:23","date_gmt":"2025-02-24T04:03:23","guid":{"rendered":"https:\/\/vingnanam.jfn.ac.lk\/?p=570"},"modified":"2025-02-24T04:03:23","modified_gmt":"2025-02-24T04:03:23","slug":"a-new-approach-to-find-integral-solutions-for-the-mordells-equation-%f0%9d%91%a62-2-%f0%9d%91%a5-3","status":"publish","type":"post","link":"https:\/\/vingnanam.jfn.ac.lk\/?p=570","title":{"rendered":"A New Approach to Find Integral Solutions for the Mordell\u2019s Equation, \ud835\udc66^2 + 2 = \ud835\udc65^ 3"},"content":{"rendered":"<h4>Authors<\/h4>\n<p>E. M. P Ekanayake, P. M. N Dharmawardane<\/p>\n<h4>Abstract<\/h4>\n<div>\n<p>Mordell\u2019s equation, y<sup>2<\/sup>+2 = x<sup>3<\/sup>, which is historically important, was solved using complex numbers and more specifically using the unique factorization method. In this paper, it is shown that Mordell\u2019s equation can be solved by using elementary mathematics and the Fermat\u2019s little theorem. In the first step, it is shown that if (x,y) is a solution of the aforementioned equation then x \u2260y and then the equation is reduced to a cubic equation. In the next step, it is shown that this cubic equation has no other integer solution than\u00a0 \u00a0using very elementary mathematics and the Fermat\u2019s little theorem, and hence the Mordell\u2019s equation has only the well-known solution x=3, y= \u00b1 5.<\/p>\n<h4>Download<\/h4>\n<p><a href=\"https:\/\/vingnanam.jfn.ac.lk\/wp-content\/uploads\/2025\/02\/16-2-1.pdf\">Article [PDF]<\/a><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Authors E. M. P Ekanayake, P. M. N Dharmawardane Abstract Mordell\u2019s equation, y2+2 = x3, which is historically important, was solved using complex numbers and more specifically using the unique factorization method. In this paper, it is shown that Mordell\u2019s equation can be solved by using elementary mathematics and the Fermat\u2019s little theorem. In the [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[305],"tags":[337,335,338,339,340,336,341],"class_list":["post-570","post","type-post","status-publish","format-standard","hentry","category-16-2","tag-cubic-equation","tag-e-m-p-ekanayake","tag-elementary-mathematics","tag-fermats-little-theorem","tag-mordells-equation","tag-p-m-n-dharmawardane","tag-unique-factorization-method"],"blocksy_meta":[],"_links":{"self":[{"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=\/wp\/v2\/posts\/570","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=570"}],"version-history":[{"count":1,"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=\/wp\/v2\/posts\/570\/revisions"}],"predecessor-version":[{"id":576,"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=\/wp\/v2\/posts\/570\/revisions\/576"}],"wp:attachment":[{"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=570"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=570"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/vingnanam.jfn.ac.lk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=570"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}