一类无非平凡有理整点的椭圆曲线y^2=x(x-p)(x-q)

A Type of Elliptic Curves y^2= x( x-p)( x-q) with no Nontrivial Integer Points

令p、q为两个素数,且p+4=q。本文证明了椭圆曲线y2=x(x-p)(x-q)没有非平凡有理整点.同时得到了一类无整解的负Pell方程组和一类无整解的四次丢番图方程.

It is shown that the type of elliptic curves y2= x（ x- p）（ x- q） have no nontrivial integer points,provided the two primes p and q satisfy p ＋ 4 = q. Based on this,we get a type of simultaneous negative Pell equations and a type of quartic Diophantine equations,which have no solutions either.