English

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.

Keywords

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}
}