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22 September 2020
 
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On odd covering systems with distinct moduli
Song Guo ; Zhi-Wei Sun ;
Date 10 Dec 2004
Journal Adv. Appl. Math. 35(2005), 182--187
Subject Number Theory; Combinatorics MSC-class: 11B25; 11A07; 11B75 | math.NT math.CO
AbstractA famous unsolved conjecture of P. Erdos and J. L. Selfridge states that there does not exist a covering system {a_s(mod n_s)}_{s=1}^k with the moduli n_1,...,n_k odd, distinct and greater than one. In this paper we show that if such a covering system {a_s(mod n_s)}_{s=1}^k exists with n_1,...,n_k all square-free, then the least common multiple of n_1,...,n_k has at least 22 prime divisors.
Source arXiv, math.NT/0412217
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