Covering the set of integers by congruence classes of distinct moduli

A set of congruences is called a covering set if every integer belongs to at least one of the congruences. Erdös has raised the following question: given any number N, does there exist a covering set of distinct moduli such that the least of such moduli is N. This has been answered in the affirmative for N up to 9. The aim of this paper is to show that there exists a covering set of distinct moduli the least of which is 20. Recently, Krukenberg independently and by other methods has also obtained results up through $N = 18$.