设a,b是正整数.我们研究了联立Pell方程组x~2-ay~2=1,y~2-bz~2=1的正整数解(x,y,z)的个数.本文利用Bennett关于联立Padé逼近的一个结果,证明了该方程组至多只有两组正整数解(x,y,z),从而改进了Bennett(1998),袁平之(2004)等人的结论.

Let a and b be positive integers.In this paper,we prove that the simulta- neous Pell equations x~2-ay~2=1,y~2-bz~2=1 possess at most two positive integer solutions (x,y,z).This result follow from a combination of the techniques including simultaneous Padéapproximation to binomial functions.It improves the previous work of Bennett (1998) and Yuan (2004).