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

被引：0

作者：

Zhang, Jin ^{[1
]}

Li, Xiaoxue ^{[2
]}

机构：

[1] Univ Arts & Sci, Sch Math & Comp Engn, Xian, Shaanxi, Peoples R China

[2] NW Univ Xian, Dept Math, Xian 710069, Shaanxi, Peoples R China

来源：

JOURNAL OF INEQUALITIES AND APPLICATIONS | 2014年

关键词：

elliptic curve; integer point; Diophantine equation;

D O I：

10.1186/1029-242X-2014-104

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let p be a fixed prime and r be a fixed positive integer. Further let N(p(2r)) denote the number of pairs of integer points (x, +/- y) on the elliptic curve E : y(2) = x(3) + p(2r)x with y > 0. Using some properties of Diophantine equations, we give a sharper upper bound estimate for N(p(2r)). That is, we prove that N(p(2r)) <= 1, except with N(17(2(2s+ 1))) = 2, where s is a nonnegative integer.

引用

页数：6

共 38 条

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[38] On the family of elliptic curves y2=x3-m2x+p2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varvec{y^2=x^3-m^2x+p^2}$$\end{document}
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