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

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.
Old Node ID: 
3873
MSC Codes: 
11A07
Author(s): 
John W. Hoffman (Kent State University) and W. Ryan Livingston (University of Georgia) and Jared Ruiz (University of Nebraska)
Publication Date: 
Monday, April 9, 2012
Original Publication Source: 
Mathematics Magazine
Original Publication Date: 
June, 2011
Subject(s): 
Congruences
Number Theory
Algebra and Number Theory
Topic(s): 
Congruences, Covering Systems
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Publish Page: 
Furnished by JSTOR: 
File Content: 
Rating Count: 
68.00
Rating Sum: 
234.00
Rating Average: 
3.44
Applicable Course(s): 
4.3 Number Theory
Modify Date: 
Saturday, August 25, 2012
3.45
Average: 3.5 (68 votes)

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