椭圆曲线y^2=nx(x^2+16)的整数点

Integral Points on Elliptic Curve y^2= nx( x^2+16)

如果n为无平方因子的正奇数,n的所有素奇数p_j(j∈Z^+)都满足P_j≡3,7(mod 8)为奇素数.本文主要利用同余、勒让德符号的性质等证明了椭圆曲线y^2=nx(x^2+16)当n≡3,7(mod 8)为奇素数时除整点(0,0)以外,至多只有两组整数点.

Let ＂n＂be a square-free positive odd number,in which prime factors could be Pj≡3,7（ mod8）,（ j∈Z＋）.It is proved the elliptic curve y2= nx（ x2＋ 16） has only two positive integer points except（ 0,0） by some properties of congruence and Legendre symbol.