关于不定方程组x^2-6y^2=1与y^2-Dz^2=4的公解

On the system of Diophantine equations x^2-6y^2=1 and y^2-Dz^2=4

设p1,…,ps(1≤s≤4)是互异的奇素数.证明了当D=2p1…ps,1≤s≤4时除开D为2×11×97外,不定方程组x2-6y2=1与y2-Dz2=4仅有平凡解(x,y,z)=(±5,±2,0).

Let p1,…,ps（1≤s≤4）are distinct odd primes.In this paper,we proved that if D=2p1 …Ps,1≤s≤4,then the system x^2-6y^2 =1andy^2-Dz^2=4 has only trivial solution （x,y,z） =（±5,±2,0）with the exception that D=2 × 11 × 97.