关于Pell方程组x^2-s^2(s^2-1)y^2=1与y^2-Dz^2=4的解

On the Solutions of System of Pell Equations x^2-s^2(s^2-1)y^2=1 and y^2-Dz^2=4

设D=p_1…p_j(1≤j≤3),p_1,…,p_j(1≤j≤3)是互异的奇素数.利用初等方法讨论了Pell方程组x^2-s^2(s^2-1)y^2=1(s∈Z+,s≥2)与y^2-Dz^2=4的解的情况.

Let D be not a perfect square positive integer which has at most three distinct prime factors. The integer solutions of the system of Pell equations in title are discussed with the help of the elementary method.