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A set of congruences is called a covering set if every integer belongs to at least one of the congruences. Erdos 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 inde- pendently and by other methods has also obtained results up through N = 18.

Covering the set of integers by congruence classes of distinct moduli