## 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

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag