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**Zentralblatt MATH**

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

**Zbl.No: ** 413.10049

**Autor: ** Erdös, Paul; Sárközy, András

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

**Source: ** Bull. Greek Math. Soc. 18, 204-223 (1977).

**Review: ** This paper continues the authors' investigation of difference and sum intersector sets and the solubility of related equations begun in part I [J. Number Theory 10, 430-450 (1978; Zbl 404.10029)]. They prove that the set **{**[\alpha],[2\alpha],...,[n\alpha],...**}** where \alpha is a fixes irrational number and [x] is the integer part of the real number x, is a difference intersector set but need not be a sum intersector set. ''Sparse'' intersector sets are also investigated and it is shown that while there are bounded difference intersector sets, sum intersector sets are always unbounded. A number of conjectures are made.

**Reviewer: ** M.M.Dodson

**Classif.: ** * 11B13 Additive bases

11B83 Special sequences of integers and polynomials

11P99 Additive number theory

11D85 Representation problems of integers

**Keywords: ** sequences of integers; density; sum intersector sets; difference intersector set

**Citations: ** Zbl.404.10029

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