  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.
