Computations and observations on congruence covering systems
Number Theory
2023-08-24 v3
Abstract
A is a collection of integer congruences such that every integer satisfies at least one congruence in the collection. A covering system is called 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 , which is .
Cite
@article{arxiv.2208.09720,
title = {Computations and observations on congruence covering systems},
author = {Raj Agrawal and Prarthana Bhatia and Kratik Gupta and Powers Lamb and Andrew Lott and Alex Rice and Christine Rose Ward},
journal= {arXiv preprint arXiv:2208.09720},
year = {2023}
}
Comments
6 pages, one table, some expository portions removed, paper reorganized to focus on Propositions 1.2 and 3.2, to appear in Proceedings of INTEGERS 2023