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Proceedings  NCUR VIII. (1994), Vol. II, pp. 794798. Jeffrey F. Gold Department of Mathematics, Department of Physics University of Utah Don H. Tucker Department of Mathematics University of Utah In this paper we present some preliminary results on a conjecture by Paul Erdos concerning covering sets of congruences. A covering set consists of a finite system of congruences with distinct moduli, such that every integer satisfies as a minimum one of the congruences. An interesting consequence of this conjecture is the dependence of the solution on abundant numbers; an abundant number is an integer whose sum of its proper divisors exceeds the integer.
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