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arXiv · 2204.09403

Congruences for sums of powers of an integer

Leif Jacob·Burkhard Külshammer
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Abstract

For coprime positive integers $q$ and $e$, let $m(q,e)$ denote the least positive integer $t$ such that there exists a sum of $t$ powers of $q$ which is divisible by $e$. We prove an upper bound for $m(q.e)$ and investigate the case where $m(q,e)$ is "large". We also pay special attention to the situation where $e$ is a prime power.

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Leif Jacob, Burkhard Külshammer. 2022-04-20. Congruences for sums of powers of an integer. https://arxiv.org/abs/2204.09403

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