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

 

On sums and products of integers


Author: Yong-Gao Chen
Journal: Proc. Amer. Math. Soc. 127 (1999), 1927-1933
MSC (1991): Primary 11B05, 11B13, 11B75, 11P99, 05A17
Published electronically: February 11, 1999
MathSciNet review: 1600124
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Abstract: Erdös and Szemerédi proved that if $A$ is a set of $k$ positive integers, then there must be at least $ck^{1+\delta}$ integers that can be written as the sum or product of two elements of $A$, where $c$ is a constant and $\delta>0$. Nathanson proved that the result holds for $\delta=\frac 1{31}$. In this paper it is proved that the result holds for $\delta=\frac 15$ and $c=\frac 1{20}$.


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Additional Information

Yong-Gao Chen
Affiliation: Department of Mathematics, Nanjing Normal University, Nanjing 210097, People’s Republic of China
Email: ygchen@pine.njnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04833-9
PII: S 0002-9939(99)04833-9
Keywords: Additive number theory, sumsets, sums and products of integers
Received by editor(s): September 24, 1997
Published electronically: February 11, 1999
Additional Notes: This research was supported by the Fok Ying Tung Education Foundation and the National Natural Science Foundation of China
Communicated by: David E. Rohrlich
Article copyright: © Copyright 1999 American Mathematical Society