Sets of sums and differences. (English) Zbl 0548.10038

Ruzsa, Imre Z.

Séminaire de théorie des nombres, Paris 1982-83, Prog. Math. 51, 267-273 (1984).

[For the entire collection see Zbl 0541.00003.]
This is a short survey about problems on sumsets and difference sets. The only new result is the construction of a set H of natural numbers which has \(O(x^{1/2+\epsilon})\) elements up to x and which is sum- intersective, that is every set of positive density has two elements the sum of which belongs to H.

MSC:

11B05	Density, gaps, topology
11B13	Additive bases, including sumsets
05B10	Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)

Keywords:

survey; sumsets; difference sets; sum-intersective