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

[31] ON THE DIOPHANTINE EQUATION x2 + x+1=yz
Schinzel, A.
COLLOQUIUM MATHEMATICUM, 2015, 141 (02) : 243 - 248
[32] The Diophantine equation X2-db2Y4=1
Walsh, G
ACTA ARITHMETICA, 1998, 87 (02) : 179 - 188
[33] A Note on the Diophantine Equation x2 + y6 = ze, e ≥ 4
Zelator, Konstantine
CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 2012, 55 (02): : 435 - 440
[34] On the Diophantine equation x2 − kxy + y2 − 2n = 0
Refik Keskin
Zafer Şiar
Olcay Karaatli
Czechoslovak Mathematical Journal, 2013, 63 : 783 - 797
[35] On the Diophantine equation x2 - kxy plus y2-2n=0
Keskin, Refik
Siar, Zafer
Karaatli, Olcay
CZECHOSLOVAK MATHEMATICAL JOURNAL, 2013, 63 (03) : 783 - 797
[36] DIOPHANTINE EQUATION X4 + Y4=2(U4 + V4)
Izadi, Farzali
Nabardi, Kamran
MATHEMATICA SLOVACA, 2016, 66 (03) : 557 - 560
[37] On the diophantine equation D(1)x(4)-D(2)y(2)=1
Le, MH
ACTA ARITHMETICA, 1996, 76 (01) : 1 - 9
[38] On the Diophantine equation X2-(22m+1)Y4=-22m
Stoll, Michael
Walsh, P. G.
Yuan, Pingzhi
ACTA ARITHMETICA, 2009, 139 (01) : 57 - 63
[39] A note on the diophantine equation (an − 1)(bn − 1) = x2
Guo Xiaoyan
Periodica Mathematica Hungarica, 2013, 66 : 87 - 93
[40] A note on the ternary Diophantine equation x2 - y2m = zn
Berczes, Attila
Le, Maohua
Pink, Istvan
Soydan, Gokhan
ANALELE STIINTIFICE ALE UNIVERSITATII OVIDIUS CONSTANTA-SERIA MATEMATICA, 2021, 29 (02): : 93 - 105