椭圆曲线y^2=qx(x^2-128)的整数点

Integral Points on Elliptic Curve y^2=qx(x^2-128)

设q为无平方因子的正奇数,q的任意素因子q_j(j∈Z+)都满足q_j≡5(mod8)。利用同余和奇偶数的性质以及勒让德符号等方法,证明了椭圆曲线y^2=qx(x^2-128)当q_j≡5(mod8)为奇素数时,除整点(x,y)=(0,0)以外至多只有两组整数点。

Let“q”be an positive odd number,Which prime factors could be q j≡5(mod8)(j∈Z^+).It was proved the elliptic curve y^2=qx(x^2-128)has only two positive integer points except(x,y)=(0,0)by some properties of congruence and Legendre symbol.