关于椭圆曲线y^2=qx(x^2+32)的正整数点

The Positive Integral Points on the Elliptic Curve y^2=qx(x^2+32)

设q为无平方因子的正奇数,q的任意素因子q_i(i∈Z^+)都满足q_i≡5(mod 8),主要利用同余的性质、Legendre符号等证明了y^2=qx(x^2+32)无正整数点.

Let q be a positive odd number,which has no square factor,and prime factors qi（i∈Z＋） satisfy qi≡5（ mod 8）.It was proved that y2= qx（x2＋32） has no positive integer points by using some properties of congruence,Legendre symbol.