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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
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