Abstract

Let $q_1,\dots <!--FUNCTION\; APPLICATION-->,q_t$ be distinct prime numbers. Let $a_1,\dots <!--FUNCTION\; APPLICATION-->,a_t$ be nonnegative integers. We establish effective lower bounds for $|z^d-q_1^{a_1}\cdots q_t^{a_t}|$ and for its greatest prime factor, which tend to infinity with $z^d$, where $z$ is a positive integer coprime with $q_1\cdots q_t$ and $d\ge 2$ is an integer.

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