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].
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页码：292 / 302
页数：11
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