Word equations with kth powers of variables

Abstract

<p>We prove that if the equality of words holds for three positive values of k, then it holds for all values of k. As a consequence, if holds for three positive values of k, then the words are powers of a common word. The most important method in our proofs is to assign numerical values to the letters, and then study the sums of the letters of words and their prefixes.<br /></p>