On D(-1)-triples {1, 4p2+1, 1-p} in the ring Z[√-p] with a prime p

被引：0

作者：

Filipin, Alan ^{[1
]}

Bokun, Mirela Jukic ^{[2
]}

Soldo, Ivan ^{[2
]}

机构：

[1] Univ Zagreb, Fac Civil Engn, Fra Andrije Kacica-Miosica 26, HR-10000 Zagreb, Croatia

[2] Univ Osijek, Dept Math, Trg Ljudevita Gaja 6, HR-31000 Osijek, Croatia

来源：

PERIODICA MATHEMATICA HUNGARICA | 2022年 / 85卷 / 02期

关键词：

Diophantine tuples; Quadratic field; Simultaneous Pellian equations; Linear form in logarithms; EXTENSIBILITY; EXTENDIBILITY; FORMS; 4K;

D O I：

10.1007/s10998-021-00435-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p be a prime such that 4p(2)+ 1 is also a prime. In this paper, we prove that the D(-1)-set {1, 4p(2) + 1, 1- p} cannot be extended with the forth element d such that the product of any two distinct elements of the new set decreased by 1 is a square in the ring Z[root-p].

引用

页码：292 / 302

页数：11

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