Baker 方法的若干应用(Ⅹ)

Applications of the Baker Method (X)

设 a.b 是给定的非零整数,p 是素数,s_p 是 p 次本原单位根.本文运用 Baker 方法证明了:当 p>C时,a-bs_p 都不是平方数,这里 C 是仅与 a,b 有关的可计算常数.

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.