{"id":381,"date":"2025-07-19T22:50:21","date_gmt":"2025-07-19T22:50:21","guid":{"rendered":"http:\/\/blogs.scienceforums.net\/pengkuan\/?p=381"},"modified":"2025-07-19T22:50:21","modified_gmt":"2025-07-19T22:50:21","slug":"classification-of-pythagorean-triples-and-reflection-on-fermats-last-theorem","status":"publish","type":"post","link":"http:\/\/blogs.scienceforums.net\/pengkuan\/2025\/07\/19\/classification-of-pythagorean-triples-and-reflection-on-fermats-last-theorem\/","title":{"rendered":"Classification of Pythagorean triples and reflection on Fermat\u2019s last theorem"},"content":{"rendered":"\n<p><\/p>\n\n\n\n<p>Kuan Peng, July 2025 \u00ab Classification of Pythagorean triples and reflection on Fermat\u2019s last theorem\u00bb<br>Pythagorean triples are generated with Euclid\u2019s formula. But how this formula was derived by or before Euclid is a mystery. We have derived Euclid\u2019s formula directly from Pythagorean equation and classified all Pythagorean triples in a 3D table. The equation<br>X^2+Y^j=Z^2 is proven to have infinitely many integer solutions. By comparing Pythagorean equation with Fermat\u2019s equation for n=3 we were able to explain why Fermat\u2019s equation with n=2 has integer solutions while with n &gt; 3 it has not. We propose an algebraic method to work Fermat\u2019s last theorem.<\/p>\n\n\n\n<p><a href=\"https:\/\/pengkuanonmaths.blogspot.com\/2025\/07\/classification-of-pythagorean-triples.html\">https:\/\/pengkuanonmaths.blogspot.com\/2025\/07\/classification-of-pythagorean-triples.html<\/a><\/p>\n\n\n\n<p><a href=\"https:\/\/www.academia.edu\/142979887\/Classification_of_Pythagorean_triples_and_reflection_on_Fermats_last_theorem\">https:\/\/www.academia.edu\/142979887\/Classification_of_Pythagorean_triples_and_reflection_on_Fermats_last_theorem<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Kuan Peng, July 2025 \u00ab Classification of Pythagorean triples and reflection on Fermat\u2019s last theorem\u00bbPythagorean triples are generated with Euclid\u2019s formula. But how this formula was derived by or before Euclid is a mystery. We have derived Euclid\u2019s formula directly &hellip; <a href=\"http:\/\/blogs.scienceforums.net\/pengkuan\/2025\/07\/19\/classification-of-pythagorean-triples-and-reflection-on-fermats-last-theorem\/\">Continue reading <span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":5,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-381","post","type-post","status-publish","format-standard","hentry","category-uncategorized"],"_links":{"self":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/381","targetHints":{"allow":["GET"]}}],"collection":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/comments?post=381"}],"version-history":[{"count":3,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/381\/revisions"}],"predecessor-version":[{"id":385,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/posts\/381\/revisions\/385"}],"wp:attachment":[{"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/media?parent=381"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/categories?post=381"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/blogs.scienceforums.net\/pengkuan\/wp-json\/wp\/v2\/tags?post=381"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}