关于Pell方程x^2-2y^2=1与y^2-Dz^2=4的公解

On the integer solution of Pell's equation x^2-2y^2=1 and y^2-Dz^2=4

设p1,…,ps是不同的奇素数,证明了当D=2p1…ps,1≤s≤6时,除了D为2×17,2×3×5×7×11×17及2×17×113×239×337×577×665857外,不定方程组仅有平凡解(x,y,z)=(±3,±2,0).

In this paper,let p1,…,ps are diverse odd primes.the following conclusion are proved：If D=2p1…ps,1≤s≤6,then the Pell equations has only trivial solutions（x,y,z）=（±3,±2,0）,with the exceptions that D=2×17,D=2×3×5×7×11×17,and D=2×17×113×239×337×577×665857.