Baker方法的若干应用(Ⅸ)

Applications of the Baker Method (Ⅸ)

设 D 是非平方正整数,k 是适合k >1,2■k 以及 gcd(D,k)=1的正整数.本文运用Baker方法证明了:方程 x^2-D=k^n 至多有2ω(k)^(+1k)组正整数解(x,n),其中w(k)是k的不同素因子的个数.

Let D be a non-square integer with D>0,and let k be a positive integ er such that k>1,2(?)k and gcd(D,k)=1. In this paper,with the ap-plication of the Baker method,we prove that the equation x^2-D=k^n has at most 2^(w(h)+1) positive integer solutions(x,n),where ω(k),is t-he number of distinct prime factors of k.