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arXiv · 2101.10415

On sparse perfect powers

Alessio Moscariello
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Abstract

This work is devoted to proving that, given an integer $x \ge 2$, there are infinitely many perfect powers, coprime with $x$, having exactly $k \ge 3$ non-zero 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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Alessio Moscariello. 2021-01-25. On sparse perfect powers. https://doi.org/10.2140/moscow.2021.10.261

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