English

An upper bound for the minimum modulus in a covering system with squarefree moduli

Number Theory 2022-11-17 v1

Abstract

Based on work of P. Balister, B. Bollob\'as, R. Morris, J. Sahasrabudhe and M. Tiba, we show that if a covering system has distinct squarefree moduli, then the minimum modulus is at most 118. We also show that in general the kthk^{\rm th} smallest modulus in a covering system with distinct moduli (provided it is required for the covering) is bounded by an absolute constant.

Cite

@article{arxiv.2211.08548,
  title  = {An upper bound for the minimum modulus in a covering system with squarefree moduli},
  author = {Maria Cummings and Michael Filaseta and Ognian Trifonov},
  journal= {arXiv preprint arXiv:2211.08548},
  year   = {2022}
}
R2 v1 2026-06-28T05:59:44.484Z