Extreme Covering Systems of the Integers
Number Theory
2022-02-11 v2
Abstract
It is proved that if the least modulus of a distinct covering system is 4, its largest modulus is at least 60; also if the least modulus is 3, the LCM of the moduli is at least 120; finally, if the least modulus is 4, the LCM of the moduli is at least 360. The constants 60, 120, and 360 can not be replaced by larger constants.
Cite
@article{arxiv.1905.07386,
title = {Extreme Covering Systems of the Integers},
author = {Jack Dalton and Ognian Trifonov},
journal= {arXiv preprint arXiv:1905.07386},
year = {2022}
}