2022/12/02 by Klein, Jonah, Koukoulopoulos, Dimitris, Lemieux, Simon
#11B25 #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.2212.01299
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, Bollobás, Morris, Sahasrabudhe and Tiba gave a simpler and more versatile proof of Hough's result. Building upon their work, we show that there exists some absolute constant c>0 such that the j-th smallest modulus of a minimal covering system with distinct moduli is ≤ exp(cj2/log(j+1)).