关于Pell方程组y^2-Dz^2=1,x^2-2Dz^2=1的正整数解

On positive integer solutions to the simultaneous Pell equations y^2-Dz^2=1 and x^2-2Dz^2=1

令D是无平方因子正整数.ω(D)表示D的不同素因子的个数.该文证明了:如果ω(D)=7,那么Pell方程组y2-Dz2=1,x2-2Dz2=1没有正整数解(x,y,z).从而改进了董晓蕾等人的结果.

Let Dbe positive square-free integers.ω(D)denotes the number of distinct prime factors of D.In this paper,we prove that ifω(D)= 7,then the system of simultaneous Pell equations y2-Dz2=1 and x2-2 Dz2=1 has no solutions in positive integers(x,y,z),which improves the result of X L Dong.