There Are Infinitely Many Rational Diophantine Sextuples

被引：30

作者：

Dujella, Andrej ^{[1
]}

Kazalicki, Matija ^{[1
]}

Mikic, Miljen ^{[2
]}

Szikszai, Marton ^{[3
]}

机构：

[1] Univ Zagreb, Dept Math, Bijenicka Cesta 30, Zagreb 10000, Croatia

[2] Kumiciceva 20, Rijeka 51000, Croatia

[3] Univ Debrecen, Inst Math, POB 12, H-4010 Debrecen, Hungary

来源：

INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2017年 / 2017卷 / 02期

关键词：

ELLIPTIC-CURVES; RANK;

D O I：

10.1093/imrn/rnv376

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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, Gibbs found the first example of a rational Diophantine sextuple. In this paper, we prove that there exist infinitely many rational Diophantine sextuples.

引用

页码：490 / 508

页数：19

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