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

Abstract

Based on work of P. Balister, B. Bollobás, 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 $k^{\mathrm{th}}$ smallest modulus in a covering system with distinct moduli (provided it is required for the covering) is bounded by an absolute constant.