The upper bound estimate of the number of integer points on elliptic curves y2=x3+p2rx

被引：0

作者：

Jin Zhang

Xiaoxue Li

机构：

[1] University of Arts and Science,School of Mathematics and Computer Engineering

[2] Northwest University,Department of Mathematics

来源：

Journal of Inequalities and Applications | / 2014卷

关键词：

elliptic curve; integer point; Diophantine equation;

D O I：

暂无

中图分类号：

学科分类号：

摘要：

Let p be a fixed prime and r be a fixed positive integer. Further let N(p2r) denote the number of pairs of integer points (x,±y) on the elliptic curve E:y2=x3+p2rx with y>0. Using some properties of Diophantine equations, we give a sharper upper bound estimate for N(p2r). That is, we prove that N(p2r)≤1, except with N(172(2s+1))=2, where s is a nonnegative integer.

引用

共 47 条

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Zhang, Jin
Li, Xiaoxue
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
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Li, Xiaoxue
JOURNAL OF INEQUALITIES AND APPLICATIONS, 2014,
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Su Gou
Xiaoxue Li
Journal of Inequalities and Applications, 2014
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PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2018, 128 (05):
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JOURNAL OF NUMBER THEORY, 2004, 109 (01) : 1 - 26
[10] ON THE FAMILY OF ELLIPTIC CURVES Y2 = X3 - T2X+1
Tadic, Petra
GLASNIK MATEMATICKI, 2012, 47 (01) : 81 - 93

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