Sums and products from a finite set of real numbers. (English) Zbl 0908.11008

Ford, Kevin

Ramanujan J. 2, No. 1-2, 59-66 (1998).

Let \(A\) be a set of real numbers. Put \(hA=\{x_1+x_2+ \cdots +x_h \mid x_i\in A\}\) and \(A^h=\{x_1x_2 \cdots x_h \;| \;x_i\in A\}\). The author deals with a conjecture of P. Erdős stating that \(hA\cup A^h\) has large cardinality. As observed at the end of the paper, the best results known on this conjecture are due to G. Elekes [Acta Arith. 81, 365-367 (1997; Zbl 0887.11012)].

Reviewer: Y.O.Hamidoune (Paris)

MSC:

11B75

Other combinatorial number theory

Keywords:

sumsets; cardinality

Citations:

Zbl 0887.11012