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ON m-COVERS AND m-SYSTEMS

Published online by Cambridge University Press:  05 October 2009

ZHI-WEI SUN
Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China (email: zwsun@nju.edu.cn)
Corresponding
E-mail address:
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Abstract

Let 𝒜={as(mod ns)}ks=0 be a system of residue classes. With the help of cyclotomic fields we obtain a theorem which unifies several previously known results related to the covering multiplicity of 𝒜. In particular, we show that if every integer lies in more than m0=⌊∑ ks=11/ns⌋ members of 𝒜, then for any a=0,1,2,… there are at least subsets I of {1,…,k} with ∑ sI1/ns=a/n0. We also characterize when any integer lies in at most m members of 𝒜, where m is a fixed positive integer.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

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