椭圆曲线y²=(x+2)(x²-2x+p)的整数点
The Integral Points on the Elliptic Curve y²=(x+2)(x²-2x+p)

利用Legendre符号、同余式、Pell方程的解的性质等初等方法证明了:当p=36s²-5(s∈$\mathbb{Z}$₊, 2？s), 而6s²-1, 12s²+1均为素数时, 椭圆曲线y²=(x+2)(x²-2x+p)仅有整数点为(x, y)=(-2, 0).
Let p=36s²-5(s∈$\mathbb{Z}$₊, 2？s), where is a positive odd number satisfying that 6s²-1 and 12s²+1 are primes. It is proved in this paper with the help of the Legendre symbol, congruence and some properties of the solutions to the Pell equation that the elliptic curve y²=(x+2)(x²-2x+p) has only integer point (x, y)=(-2, 0)