Signed sums of terms of a sequence

Authors:
Feng-Juan Chen and Yong-Gao Chen

Journal:
Proc. Amer. Math. Soc. **141** (2013), 1105-1111

MSC (2010):
Primary 11A67, 11B50, 11B83, 11P05

DOI:
https://doi.org/10.1090/S0002-9939-2012-11397-8

Published electronically:
August 9, 2012

MathSciNet review:
3008858

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Abstract | References | Similar Articles | Additional Information

Abstract: We give a sufficient and necessary condition on the sequence of integers that for any integer , every integer can be represented in the form , where . This generalizes the known result on integral-valued polynomial values. Moreover, we show that such sequences exist with any growth rate. This answers two problems posed by Bleicher. We also pose several problems for further research.

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Additional Information

**Feng-Juan Chen**

Affiliation:
School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210046, People’s Republic of China – and – Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China

Email:
cfjsz@126.com

**Yong-Gao Chen**

Affiliation:
School of Mathematical Sciences and Institute of Mathematics, Nanjing Normal University, Nanjing 210046, People’s Republic of China

Email:
ygchen@njnu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-2012-11397-8

Keywords:
Signed sums,
sequences,
polynomials

Received by editor(s):
March 14, 2011

Received by editor(s) in revised form:
August 4, 2011

Published electronically:
August 9, 2012

Additional Notes:
This work was supported by the National Natural Science Foundation of China, Grant No. 11071121 and the Project of Graduate Education Innovation of Jiangsu Province (CXZZ11-0868).

Communicated by:
Matthew A. Papanikolas

Article copyright:
© Copyright 2012
American Mathematical Society

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