Pell方程x^2-2y^2=1和y^2-Dz^2=4的公解

On the Solutions of the Pell Equation x^2-2y^2=1 and y^2-Dz^2=4

本文证明了当D模12不同余-1且D为7或者8个不同奇素数之积时,Pell方程x2-2y2=1和y2-Dz2=4仅有平凡解z=0.

In this paper,the following conclusion is proved： If D≠-1（ mod 12） and D0 is an odd squarefree integer which has 7 or 8 distinct prime factors,the equation x^2-2y^2= 1 and y-Dz^2= 4 has only one trivial solution z = 0.