In 1952, H. Davenport posed the problem of determining a condition on the minimum modulus m 0 m₀ in a finite distinct covering system that would imply that the sum of the reciprocals of the moduli in the covering system is bounded away from 1 1. In 1973, P. Erdős and J. Selfridge indicated that they believed that m 0 > 4 m₀ > 4 would suffice. We provide a proof that this is the case.
Filaseta et al. (Thu,) studied this question.