On the diophantine equation X2 − (1 + a2)Y4 = −2a

被引：0

作者：

PingZhi Yuan

ZhongFeng Zhang

机构：

[1] South China Normal University,School of Mathematics

[2] Sun Yat-Sen University,School of Mathematics & Computational Science

来源：

Science China Mathematics | 2010年 / 53卷

关键词：

algebraic approximations; continued fractions; elliptic curves; quartic equations; 11B39; 11D41;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let a ⩾ 1 be an integer. In this paper, we will prove the equation in the title has at most three positive integer solutions.

引用

页码：2143 / 2158

页数：15

共 50 条

[41] A note on the Diophantine equation x2 + qm = y3
Zhu, Hui Lin
ACTA ARITHMETICA, 2011, 146 (02) : 195 - 202
[42] ON THE DIOPHANTINE EQUATION Z(2) = X(4)+DX(2)Y(2)+Y(4)
COHN, JHE
GLASGOW MATHEMATICAL JOURNAL, 1994, 36 : 283 - 285
[43] ON THE DIOPHANTINE EQUATION X4+/-Y4=ZP
POWELL, B
BULLETIN DES SCIENCES MATHEMATIQUES, 1983, 107 (02): : 219 - 223
[44] On the Diophantine equation x4 + y4 = c
Bremner, Andrew
Tho, Nguyen Xuan
ACTA ARITHMETICA, 2022, : 141 - 150
[45] DIOPHANTINE EQUATION X2 + D=4YQ
LJUNGGREN, W
MONATSHEFTE FUR MATHEMATIK, 1971, 75 (02): : 136 - +
[46] ON THE DIOPHANTINE EQUATION X2 + D = 4PN
LE, MH
JOURNAL OF NUMBER THEORY, 1992, 41 (01) : 87 - 97
[47] On the diophantine equation (x(x-1)/2)(2)=y(y-1)/2
Luo, M
FIBONACCI QUARTERLY, 1996, 34 (03): : 277 - 279
[48] On the Diophantine equations x2 - Dy2 = -1 and x2 - Dy2 = 4
Chen, Bingzhou
Luo, Jiagui
AIMS MATHEMATICS, 2019, 4 (04): : 1170 - 1180
[49] Line lists for the X2Σ+-X2Σ+, A2Π-A2Π and A2Π-X2Σ+transitions of CP
Qin, Zhi
Bai, Tianrui
Liu, Linhua
JOURNAL OF QUANTITATIVE SPECTROSCOPY & RADIATIVE TRANSFER, 2021, 258
[50] A note on the diophantine equation ((x)(4))=((y)(2))
Pinter, AK
PUBLICATIONES MATHEMATICAE-DEBRECEN, 1995, 47 (3-4): : 411 - 415