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;
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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.
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