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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Upper bounds for finite additive $ 2$-bases


Author: Gang Yu
Journal: Proc. Amer. Math. Soc. 137 (2009), 11-18
MSC (2000): Primary 11B13
Published electronically: July 18, 2008
MathSciNet review: 2439419
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Abstract: For a positive integer $ N$, a set $ \mathcal{A}\subset [0,N]\cap\mathbb{Z}$ is called a $ 2$-basis for $ N$ if every integer $ n\in [0,N]$ can be represented as $ n=a+b$, where $ a, b\in\mathcal{A}$. In this paper, we give a lower bound estimate for the cardinality of an additive $ 2$-basis for $ N$, as $ N\to\infty$, which improves the existing results on this topic.


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Additional Information

Gang Yu
Affiliation: Department of Mathematical Sciences, Kent State University, Kent, Ohio 44242
Email: yu@math.kent.edu

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09430-6
PII: S 0002-9939(08)09430-6
Received by editor(s): June 25, 2007
Received by editor(s) in revised form: November 15, 2007
Published electronically: July 18, 2008
Additional Notes: The author was supported by NSF grant DMS-0601033.
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.