关于椭圆曲线y^2=px(x^2-2)的正整数点的一个注记

A Note on the Positive Integer Points of Elliptic Curve y^2=px(x^2-2)

利用四次剩余与Pell方程的性质,导出了椭圆曲线y^2=px(x^2-2)[p是满足p≡1(mod 8)的奇质数]的正整数点的一个性质,证明了该椭圆曲线至多有4个正整数点的结论和至多有2个正整数点的充分条件。

By using the properties of quadratic residue and Pell equation, a property of positive integer points of elliptic curve y^2=px(x^2-2) was derived,Where p was an odd prime with p≡1(mod 8) The study has proved the conclusion that this elliptic curve has at most four positive integer points and sufficient conditions for at most two positive integer points.