{"id":506,"date":"2017-03-18T14:59:25","date_gmt":"2017-03-18T12:59:25","guid":{"rendered":"http:\/\/bela.phy.hr\/quantixlie\/?p=506"},"modified":"2017-03-18T15:00:45","modified_gmt":"2017-03-18T13:00:45","slug":"there-are-infinitely-many-rational-diophantine-sextuples","status":"publish","type":"post","link":"http:\/\/bela.phy.hr\/quantixlie\/hr\/there-are-infinitely-many-rational-diophantine-sextuples\/","title":{"rendered":"There Are Infinitely Many Rational Diophantine Sextuples"},"content":{"rendered":"<p>A rational Diophantine <em>m<\/em>-tuple is a set of <em>m<\/em> non zero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple. In this paper, we prove that there exist infinitely many rational Diophantine sextuples.<\/p>\n<div class=\"ww-citation-primary\"><\/div>\n<div class=\"ww-citation-primary\">\n<div class=\"al-author-name\"><strong>Andrej Dujella,\u00a0Matija Kazalicki,\u00a0Miljen Miki\u0107,\u00a0M\u00e1rton Szikszai<\/strong><\/div>\n<div class=\"al-author-name\"><\/div>\n<\/div>\n<div class=\"al-author-name\">\n<div class=\"ww-citation-primary\"><strong>Int Math Res Notices (2017) 2017 (2): 490-508. DOI:\u00a0<a href=\"https:\/\/doi.org\/10.1093\/imrn\/rnv376\">https:\/\/doi.org\/10.1093\/imrn\/rnv376<\/a><\/strong><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<div class=\"mh-excerpt\"><p>A rational Diophantine m-tuple is a set of m non zero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus, while Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, <a class=\"mh-excerpt-more\" href=\"http:\/\/bela.phy.hr\/quantixlie\/hr\/there-are-infinitely-many-rational-diophantine-sextuples\/\" title=\"There Are Infinitely Many Rational Diophantine Sextuples\">[&#8230;]<\/a><\/p>\n<\/div>","protected":false},"author":5,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":[],"categories":[18,14],"tags":[],"_links":{"self":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/506"}],"collection":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/comments?post=506"}],"version-history":[{"count":2,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/506\/revisions"}],"predecessor-version":[{"id":508,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/posts\/506\/revisions\/508"}],"wp:attachment":[{"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/media?parent=506"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/categories?post=506"},{"taxonomy":"post_tag","embeddable":true,"href":"http:\/\/bela.phy.hr\/quantixlie\/hr\/wp-json\/wp\/v2\/tags?post=506"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}