On Diophantine Equations 2x ± (2kp)y = z2 and-2x + (2k3)y = z2

被引：0

作者：

Li, Yuan ^{[1
]}

Lloyd, Torre ^{[1
]}

Clinton, Angel ^{[1
]}

机构：

[1] Winston Salem State Univ, Dept Math, Winston Salem, NC 27110 USA

来源：

MATHEMATICS | 2024年 / 12卷 / 24期

关键词：

Catalan equation; elliptic curve;

D O I：

10.3390/math12244027

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we solve three Diophantine equations: 2x +/-(2kp)y=z2 and -2x+(2k3)y=z2 with k >= 0 and prime p equivalent to +/- 3(mod8). We obtain all the non-negative integer solutions by using elementary methods and the database of elliptic curves in "The L-functions and modular forms database" (LMFDB).

引用

页数：6

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