椭圆曲线y^(2)=(x-6)(x^(2)+6x+r)的正整数点

The Positive Integral Points on the Elliptic Curve y^(2)=(x-6)(x^(2)+6x+r)

利用同余式、Legendre符号、Pell方程的解的性质等初等方法证明了r=36t^(2)-69,t∈Z^(+),2■t,而12t^(2)+1,6t^(2)-13均为素数时椭圆曲线y^(2)=(x-6)(x^(2)+6x+r)无正整数点。

Let r=36t^(2)-69,where t is a positive odd number satisfying that 12t^(2)+1 and 6t^(2)-13 are primes.The elliptic curve in title has no positive integer points were proved with the help of congruence,Legendre symbol and some properties of the solutions to Pell equation.