Claims

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2005_07_18_filaseta_ford_konyagin_pomerance_yu: Theorem A of Filaseta, Ford, Konyagin, Pomerance and Yu (J. Amer. Math. Soc. 2007): large distinct moduli with a slowly growing reciprocal sum cannot cover, so bounded reciprocal sum bounds the minimum modulus; refereed.

2013_07_02_hough: Hough's theorem in the Annals of Mathematics (2015) that every finite covering system with distinct moduli greater than one has least modulus at most ten to the sixteenth; accepted on the refereed paper and site credit.

2018_11_08_balister_bollobas_morris_sahasrabudhe_tiba: Theorem 8.1 of the Inventiones paper (2022) shows that distinct moduli all at least 616000 cannot cover the integers, a second proof that the minimum modulus is bounded; accepted on the refereed paper and the site's credit.

2022_11_15_cummings_filaseta_trifonov: Theorem 1.1 of Cummings, Filaseta and Trifonov (Acta Math. Hungar. 2025): a covering system with distinct squarefree moduli has smallest modulus at most 118, a sharper bound for that restricted class; refereed.

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