Signed sums of terms of a sequence
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- by Feng-Juan Chen and Yong-Gao Chen PDF
- Proc. Amer. Math. Soc. 141 (2013), 1105-1111 Request permission
Abstract:
We give a sufficient and necessary condition on the sequence $\{a_n\}$ of integers that for any integer $l\ge 1$, every integer can be represented in the form $\varepsilon _l a_l+\varepsilon _{l+1} a_{l+1}+\cdots + \varepsilon _ka_k$, where $\varepsilon _i\in \{-1, 1\}\ (i=l,l+1,\ldots , k)$. 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.References
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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
- MR Author ID: 304097
- Email: ygchen@njnu.edu.cn
- 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
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 3008858