On covering multiplicity

Author:
Zhi-Wei Sun

Journal:
Proc. Amer. Math. Soc. **127** (1999), 1293-1300

MSC (1991):
Primary 11B25; Secondary 11A07, 11B75, 11D68

Published electronically:
January 27, 1999

MathSciNet review:
1486752

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be a system of arithmetic sequences which forms an -cover of (i.e. every integer belongs at least to members of ). In this paper we show the following surprising properties of : (a) For each there exist at least subsets of with such that . (b) If forms a minimal -cover of , then for any there is an such that for every there exists an for which and

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Additional Information

**Zhi-Wei Sun**

Email:
zwsun@netra.nju.edu.cn

DOI:
http://dx.doi.org/10.1090/S0002-9939-99-04817-0

Received by editor(s):
August 13, 1997

Published electronically:
January 27, 1999

Additional Notes:
Supported by the National Natural Science Foundation of the People’s Republic of China and the Return-from-abroad Foundation of the Chinese Educational Committee.

Communicated by:
David E. Rohrlich

Article copyright:
© Copyright 1999
American Mathematical Society