Congruences for sums of powers of an integer

DOI10.5486/PMD.2023.9406arXiv2204.09403MaRDI QIDQ6111839

Author name not available (Why is that?), Burkhard Külshammer

Publication date: 4 August 2023

Published in: Publicationes Mathematicae Debrecen (Search for Journal in Brave)

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.

Full work available at URL: https://arxiv.org/abs/2204.09403

zbMATH Keywords

Waring's problemsums of powerszero-sum problems

Mathematics Subject Classification ID

Waring's problem and variants (11P05) Additive bases, including sumsets (11B13) Representation problems (11D85)

Related Items (5)

Congruence properties of the function which counts compositions into powers of 2 ⋮ Title not available (Why is that?) ⋮ Congruences for Brewer sums ⋮ Title not available (Why is that?) ⋮ Title not available (Why is that?)

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