Year: 2022
Type: preprint
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 Erdős. 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 $11$.
Source: arXiv (Cornell University)
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4292956676