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A Note on Disjoint Covering Systems—Variations on a 2002 AIME Problem
by John W. Hoffman (Kent State University), W. Ryan Livingston (University of Georgia) and Jared Ruiz (University of Nebraska)
This article originally appeared in:Mathematics Magazine
June, 2011
Subject classification(s): Congruences | Number Theory | Algebra and Number Theory
Applicable Course(s): 4.3 Number Theory
A covering system is a system of \(k\) arithmetic progressions whose union includes all integers. This paper presents upper bounds on the number of consecutive integers which need to be checked to determine whether a covering system is a disjoint covering system.
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Capsule Course Topic(s): Number Theory | Congruences, Covering Systems
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