On odd covering systems with distinct moduli

2004/12/31 by Song Guo, Zhi-Wei Sun
Mathematics · #math.NT #math.CO #msc:11B25 #msc:11A07 #msc:11B75

paper · pdf

published as Adv. Appl. Math. 35(2005), 182--187 · 7 pages, final version

arxiv created 2005/09/14 · arxiv updated 2009/12/01

Abstract

A 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 n₁,...,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 n₁,...,n_k all square-free, then the least common multiple of n₁,...,n_k has at least 22 prime divisors.

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