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Covering the Set of Integers by Congruence Classes of Distinct Moduli

S. L. G. Choi
Mathematics of Computation
Vol. 25, No. 116 (Oct., 1971), pp. 885-895
DOI: 10.2307/2004353
Stable URL: http://www.jstor.org/stable/2004353
Page Count: 11
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Abstract

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.

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