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 | References | Similar Articles | Additional Information

Abstract: Erdös and Szemerédi proved that if is a set of positive integers, then there must be at least integers that can be written as the sum or product of two elements of , where is a constant and . Nathanson proved that the result holds for . In this paper it is proved that the result holds for and .

**1.**Paul Erdős,*Problems and results on combinatorial number theory. III*, Number theory day (Proc. Conf., Rockefeller Univ., New York, 1976), Springer, Berlin, 1977, pp. 43–72. Lecture Notes in Math., Vol. 626. MR**0472752****2.**P. Erdős and E. Szemerédi,*On sums and products of integers*, Studies in pure mathematics, Birkhäuser, Basel, 1983, pp. 213–218. MR**820223****3.**Melvyn B. Nathanson,*On sums and products of integers*, Proc. Amer. Math. Soc.**125**(1997), no. 1, 9–16. MR**1343715**, 10.1090/S0002-9939-97-03510-7**4.**M. B. Nathanson and G. Tenenbaum,*Inverse theorems and the number of sums and products*(to appear).

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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

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