On odd covering systems with distinct moduli
Abstract
A famous unsolved conjecture of P. Erdos and J. L. Selfridge states that there does not exist a covering system as(mod ns)s=1k with the moduli n1,...,nk odd, distinct and greater than one. In this paper we show that if such a covering system as(mod ns)s=1k exists with n1,...,nk all square-free, then the least common multiple of n1,...,nk has at least 22 prime divisors.
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