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On a conjecture of Crittenden and Vanden Eynden concerning coverings by arithmetic progressions

Part of: Sequences and sets

Published online by Cambridge University Press:  09 April 2009

R. J. Simpson
R. J. Simpson
Affiliation:
School of Mathematics Curtin University of TechnologyPerth, WA 6001Australia e-mail: [email protected]
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Abstract

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Crittenden and Vanden Eynden conjectured that if n arithmetic progressions, each having modulus at least k, include all the integers from 1 to k2n-k+1, then they include all the integers. They proved this for the cases k = 1 and k = 2. We give various necessary conditions for a counterexample to the conjecture; in particular we show that if a counterexample exists for some value of k, then one exists for that k and a value of n less than an explicit function of k.

Keywords

arithmetic progressionscovering systems.

MSC classification

Secondary: 11B25: Arithmetic progressions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 63 , Issue 3 , December 1997 , pp. 396 - 420
Copyright
Copyright © Australian Mathematical Society 1997

References

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