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).
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页数：6
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