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On a conjecture of Crittenden and Vanden Eynden concerning coverings by arithmetic progressions
Published online by Cambridge University Press: 09 April 2009
Abstract
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.
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- Research Article
- Information
- Journal of the Australian Mathematical Society , Volume 63 , Issue 3 , December 1997 , pp. 396 - 420
- Copyright
- Copyright © Australian Mathematical Society 1997
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