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arXiv · 2211.08548

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

Maria Cummings·Michael Filaseta·Ognian Trifonov
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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 $k^{\rm th}$ smallest modulus in a covering system with distinct moduli (provided it is required for the covering) is bounded by an absolute constant.

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Maria Cummings, Michael Filaseta, Ognian Trifonov. 2022-11-15. An upper bound for the minimum modulus in a covering system with squarefree moduli. https://arxiv.org/abs/2211.08548

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