Pell方程组x^2-ay^2=1和z^2-by^2=1的解数

The Number of Solutions of Pell Equations x^2-ay^2 =1 and z2-by^2 =1

设a,b是不同的正整数,本文证明了:当max(a,b)>10126时,Pell方程组X2-ay2=1 和z2-by2=1至多有2组正整数解(X,y,z).

Let a, b be distinct positive integers. In this paper we prove that if max(a, b) > 10126, then Pell equations x2-ay2=1 and z2-by2=1 have at most two positive integer solutions (x, y, z).