A1 Refereed original research article in a scientific journal

Word equations with kth powers of variables



Authors: Saarela Aleksi

Publisher: Academic Press Inc.

Publication year: 2019

Journal: Journal of Combinatorial Theory, Series A

Journal name in source: Journal of Combinatorial Theory. Series A

Volume: 165

First page : 15

Last page: 31

Number of pages: 17

ISSN: 0097-3165

DOI: https://doi.org/10.1016/j.jcta.2019.01.004

Self-archived copy’s web address: https://research.utu.fi/converis/portal/detail/Publication/39497480


Abstract

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.


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Last updated on 2024-26-11 at 13:02