Vol. 10, No. 4, 2021
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On sparse perfect powers

Alessio Moscariello
Vol. 10 (2021), No. 4, 261–270
DOI: 10.2140/moscow.2021.10.261
Abstract

This work is devoted to proving that, given an integer x ≥ 2, there are infinitely many perfect powers coprime with x having exactly k ≥ 3 nonzero digits in their base x representation, except for the case x = 2, k = 4, for which a known finiteness result by Corvaja and Zannier holds.

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Keywords
sparse powers, base representation
Mathematical Subject Classification
Primary: 11P99
Secondary: 11D41
Milestones
Received: 25 January 2021
Revised: 25 July 2021
Accepted: 11 September 2021
Published: 17 January 2022
Authors
Alessio Moscariello
Dipartimento di Matematica
Università di Pisa
Pisa
Italy