an:03641573
Zbl 0413.10049
Erd??s, Paul; S??rk??zy, Andr??s
On differences and sums of integers. II
EN
Bull. Greek Math. Soc. 18, 204-223 (1977).
00143803
1977
j
11B13 11B83 11P99 11D85
sequences of integers; density; sum intersector sets; difference intersector set
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.
M.M.Dodson
Zbl 0404.10029