On sums and products of integers
Author: Melvyn B. Nathanson
Journal: Proc. Amer. Math. Soc. 125 (1997), 9-16
MSC (1991): Primary 11B05, 11B13, 11B75, 11P99, 05A17
MathSciNet review: 1343715
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Abstract: Erdos and Szemerédi conjectured 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 . Erdos and Szemerédi proved that this number must be at least for some and . In this paper it is proved that the result holds for .
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Melvyn B. Nathanson
Affiliation: Department of Mathematics, Lehman College (CUNY), Bronx, New York 10468
Keywords: Additive number theory, sumsets, sums and products of integers
Received by editor(s): June 25, 1994
Received by editor(s) in revised form: May 23, 1995
Additional Notes: This work was supported in part by grants from the PSC-CUNY Research Award Program and the National Security Agency Mathematical Sciences Program
Communicated by: William W. Adams
Article copyright: © Copyright 1997 American Mathematical Society