# A Note on Disjoint Covering Systems—Variations on a 2002 AIME Problem

by John W. Hoffman (Kent State University) and 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