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 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.
Categories: math.NT math.CO