2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/73554A 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.7 pages, final versionNumber TheoryCombinatorics11B25; 11A07; 11B75text