## 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 a1 \leq ... \leq an} integer set there are at least f(n) distinct numbers of the form ai+aj, aiaj, 1 \leq i \leq j \leq n, the authors prove that

n1+c1 < f(n) < n2\exp(-c2 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