On the difference between perfect powers andintegral S-units

Abstract

On the difference between perfect powers and integral S-units Yann BugeaudLet q 1 , . . ., q t be distinct prime numbers.Let a 1 , . . ., a t be nonnegative integers.We establish effective lower bounds for |z d q a 1 1 • • • q a t t | and for its greatest prime factor, which tend to infinity with z d , where z is a positive integer coprime with q 1 • • • q t and d ≥ 2 is an integer.