# 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
Flag for Digital Object Identifier:
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