椭圆曲线y^2=px(x^2+2)在p≡1(mod 8)时的正整数点

The Positive Integral Points on Elliptic Curves y^2 = px(x^2 + 2) with p ≡ 1(mod 8)

设p是适合p≡1(mod 8)的奇素数.运用二次和四次Diophantine方程的性质给出了椭圆曲线E:Y^2=px(x^2+2)有正整数点(x,y)的判别条件,并且证明了:当p<100时,该曲线没有正整数点.

Let p be an odd prime with p ≡1（mod 8） . In this paper, using properties of quadratic and quartic diophantine equations, certain criterions for the elliptic curve E ： y2 = px（x2 ＋ 2） has positive integer points （x, y） are given. Moreover, we prove that if p 〈 100, then the elliptic curve has no positive integer point.