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
收藏
页码：2143 / 2158
页数：15
相关论文
共 50 条
[41]   A note on the trace of Frobenius for curves of the form y2 = x3 [J].
Walsh, P. G. .
ANNALES MATHEMATICAE ET INFORMATICAE, 2022, 55 :184-188
[42]   ON THE ELLIPTIC CURVES OF THE FORM y2 = x3-3px [J].
Daghigh, H. ;
Didari, S. .
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2014, 40 (05) :1119-1133
[43]   DEFINING EQUATIONS OF X-1(2N) [J].
Jeon, Daeyeol .
KOREAN JOURNAL OF MATHEMATICS, 2013, 21 (03) :305-309
[44]   On the elliptic curves y2=x3-c with embedding degree one [J].
Kirlar, Baris Bulent .
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (16) :4724-4728
[45]   ON THE NUMBER OF INTEGER POINTS ON THE ELLIPTIC CURVE y2 = x3+Ax [J].
Draziotis, Konstantinos A. .
INTERNATIONAL JOURNAL OF NUMBER THEORY, 2011, 7 (03) :611-621
[46]   Generators and integer points on the elliptic curve y2 = x3 - nx [J].
Fujita, Yasutsugu ;
Terai, Nobuhiro .
ACTA ARITHMETICA, 2013, 160 (04) :333-348
[47]   On the nonexistence of 2-cycles for the 3x+1 problem [J].
Simons, JL .
MATHEMATICS OF COMPUTATION, 2005, 74 (251) :1565-1572
[48]   Integer Points and Independent Points on the Elliptic Curve y2 = x3-pkx [J].
Fujita, Yasutsugu ;
Terai, Nobuhiro .
TOKYO JOURNAL OF MATHEMATICS, 2011, 34 (02) :367-381
[49]   Generators for the elliptic curve y2 = x3-nx of rank at least three [J].
Fujita, Yasutsugu .
JOURNAL OF NUMBER THEORY, 2013, 133 (05) :1645-1662
[50]   210=14x15=5x6x7=((21)(2))=((10)(4)) [J].
Pinter, A ;
deWeger, BMM .
PUBLICATIONES MATHEMATICAE-DEBRECEN, 1997, 51 (1-2) :175-189
12345