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A sum-division estimate of reals

Author(s): Liangpan Li; Jian Shen
Journal: Proc. Amer. Math. Soc. 138 (2010), 101-104.
MSC (2000): Primary 11B75
Posted: August 24, 2009
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Abstract: Let $ A$ be a finite set of positive real numbers. We present a sum-division estimate:

$\displaystyle \vert A+A\vert^2\vert A/A\vert\geq\frac{\vert A\vert^4}{4}.$

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Additional Information:

Liangpan Li
Affiliation: Department of Mathematics, Shanghai Jiao Tong University, Shanghai 200240, People's Republic of China - and - Department of Mathematics, Texas State University, San Marcos, Texas 78666
Email: liliangpan@yahoo.com.cn

Jian Shen
Affiliation: Department of Mathematics, Texas State University, San Marcos, Texas 78666
Email: js48@txstate.edu

DOI: 10.1090/S0002-9939-09-10052-7
PII: S 0002-9939(09)10052-7
Keywords: Sum-product estimate, sum-division estimate
Received by editor(s): May 12, 2009,
Received by editor(s) in revised form: May 18, 2009
Posted: August 24, 2009
Communicated by: Ken Ono
Copyright of article: Copyright 2009, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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