Covering systems in number fields

M. Filaseta, K. Ford, S. Konyagin, C. Pomerance and G. Yu proved that if the reciprocal sum of the moduli of a covering system is bounded, then the least modulus is also bounded, which confirms a conjecture of P. Erdős and J.L. Selfridge. They also showed that, for K>1, the complement in Z of any union of residue classes with distinct n∈(N,KN] has density at least dK for N sufficiently large, which implies a conjecture of P. Erdős and R.L. Graham. In this paper, we extend these results to covering systems of the ring of integers of an arbitrary number field F/Q.