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Covering systems were introduced by Erdős in 1950. In the same article where he introduced them, he asked if the minimum modulus of a covering system with distinct moduli is bounded. In 2015, Hough answered affirmatively this long standing question. In 2022, Balister et al. gave a simpler and more versatile proof of Hough’s result. Building upon their work, we show that there exists some absolute constant Formula: see text such that the Formula: see textth smallest modulus of a minimal covering system with distinct moduli is Formula: see text.
Klein et al. (Sat,) studied this question.