一类孪生素数椭圆曲线上的整数点

The integral points on a class of twin-prime elliptic curves

设p,q是适合p+2=q的孪生素数.本文讨论了椭圆曲线E:y2=x(x-2)(x+p)上的整数点(x,y),运用二次和四次D iophantine方程的性质证明:该曲线至多有一对整数点(x,±y)且y≠0.

Let p and q be twin primes with p＋2=q.the integral points（x,y） on the elliptic curve E：y^2=x（x-2）（x＋p） are discussed.Using the properties of quadratic and quartic Diophantine equations,it is proved that the elliptic curve has most one pair of integral points（x,±y） with y≠0.