Binomial coefficients and the ring of -adic integers

Authors:
Zhi-Wei Sun and Wei Zhang

Journal:
Proc. Amer. Math. Soc. **139** (2011), 1569-1577

MSC (2010):
Primary 11B65; Secondary 05A10, 11A07, 11S99

DOI:
https://doi.org/10.1090/S0002-9939-2010-10587-7

Published electronically:
October 28, 2010

MathSciNet review:
2763746

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be an integer and let be a prime. We show that if or (with ) for some , then the set is dense in the ring of -adic integers; i.e., it contains a complete system of residues modulo any power of .

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Additional Information

**Zhi-Wei Sun**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Email:
zwsun@nju.edu.cn

**Wei Zhang**

Affiliation:
Department of Mathematics, Nanjing University, Nanjing 210093, People’s Republic of China

Email:
zhangwei_07@yahoo.com.cn

DOI:
https://doi.org/10.1090/S0002-9939-2010-10587-7

Received by editor(s):
December 26, 2009

Received by editor(s) in revised form:
May 15, 2010

Published electronically:
October 28, 2010

Additional Notes:
The first author is the corresponding author. He is supported by the National Natural Science Foundation (grant 10871087) and the Overseas Cooperation Fund (grant 10928101) of China

Communicated by:
Wen-Ching Winnie Li

Article copyright:
© Copyright 2010
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.