Integral Points on the Elliptic Curve y2 = x3 − 4p2x

被引：0

作者：

Hai Yang

Ruiqin Fu

机构：

[1] Xi’an Polytechnic University,School of Science

[2] Xi’an Shiyou University,School of Science

来源：

Czechoslovak Mathematical Journal | 2019年 / 69卷

关键词：

elliptic curve; integral point; quadratic equation; quartic Diophantine equation; 11G05; 11D25; 11Y50;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let p be a fixed odd prime. We combine some properties of quadratic and quartic Diophantine equations with elementary number theory methods to determine all integral points on the elliptic curve E: y2 = x3 − 4p2x. Further, let N(p) denote the number of pairs of integral points (x, ±y) on E with y > 0. We prove that if p ⩾ 17, then N(p) ⩽ 4 or 1 depending on whether p ≡ 1 (mod 8) or p ≡ −1 (mod 8).

引用

页码：853 / 862

页数：9

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