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arXiv · 2208.09720

Computations and observations on congruence covering systems

Raj Agrawal·Prarthana Bhatia·Kratik Gupta·Powers Lamb·Andrew Lott·Alex Rice·Christine Rose Ward
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Abstract

A $\textit{covering system}$ is a collection of integer congruences such that every integer satisfies at least one congruence in the collection. A covering system is called $\textit{distinct}$ if all of its moduli are distinct. An expansive literature has developed on covering systems since their introduction by Erd\H{o}s. Here we provide a full classification of distinct covering systems with at most ten moduli, which we group together based on two forms of equivalence. As a consequence, we determine the minimum cardinality of a distinct covering system with all moduli exceeding $2$, which is $11$.

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Raj Agrawal, Prarthana Bhatia, Kratik Gupta, Powers Lamb, Andrew Lott, Alex Rice, Christine Rose Ward. 2022-08-20. Computations and observations on congruence covering systems. https://arxiv.org/abs/2208.09720

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