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On differences and sums of integers. II. (English) Zbl 0413.10049
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 0404.10029)]. They prove that the set $$\{[\alpha],[2\alpha],\dots,[n\alpha],\dots\}$$ 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

##### MSC:
 11B13 Additive bases, including sumsets 11B83 Special sequences and polynomials 11P99 Additive number theory; partitions 11D85 Representation problems