椭圆曲线y^(2)=7qx(x^(2)-2)的正整数点

Positive integer Points of Elliptic Curves y 2=7qx(x^(2)-2)

利用同余的性质、Legendre符号的性质等初等方法,证明了:若q=pΠ_(i=1)^(n)q_(i),p≡±3,±19,±27(mod56)为奇素数,q_(i)≡±3(mod8)为互异的奇素数,则椭圆曲线y2=7qx(x^(2)-2)除整数点(x,y)=(0,0)外至多有2个正整数点。

By using elementary methods such as the properties of congruence and Legendre symbols,it is proved that if q=pΠ_(i=1)^(n)q_(i),p≡±3,±19,±27(mod56) is an odd prime number and q_(i)≡±3(mod8)is a distinct odd prime number,the elliptic curve y^(2)=7qx(x^(2)-2)at most has two positive integers.