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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 526.10011

**Autor: ** Erdös, Paul; Szemeredi, E.

**Title: ** On sums and products of integers. (In English)

**Source: ** Studies in pure mathematics, Mem. of P. Turan, 213-218 (1983).

**Review: ** [This article was published in the book announced in Zbl 512.00007.]

Denoting by f(n) the largest integer such that for every **{**1 \leq a_{1} \leq ... \leq a_{n}**}** integer set there are at least f(n) distinct numbers of the form a_{i}+a_{j}, a_{i}a_{j}, 1 \leq i \leq j \leq n, the authors prove that n^{1+c1} < f(n) < n^{2}\exp(-c_{2} log n/ log log n). Some other related results and a lot of related conjectures are also discussed. The proof is self-contained and based only on elementary combinatorial arguments.

**Reviewer: ** A.Balog

**Classif.: ** * 11B75 Combinatorial number theory

11B83 Special sequences of integers and polynomials

11B13 Additive bases

**Keywords: ** sums and products of integers; combinatorial number theory; addition and multiplication of sets

**Citations: ** Zbl.512.00007

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