## Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  597.10055
Autor:  Erdös, Paul; Sárközy, A.; Sós, V.T.
Title:  Problems and results on additive properties of general sequences. V. (In English)
Source:  Monatsh. Math. 102, 183-197 (1986).
Review:  [Part I, cf. Pac. J. Math. 118, 347-357 (1985; Zbl 569.10032), part IV, cf. Lect. Notes Math. 1122, 85-104 (1985; Zbl 588.10056).]
A very special case of one of the theorems of the authors states as follows: Let 1 \leq a1 \leq a2 \leq ... be an infinite sequence of integers for which all the sums ai+aj, 1 \leq i \leq j, are distinct. Then there are infinitely many integers k for which 2k can be represented in the form ai+aj but 2k+1 cannot be represented in this form. Several unsolved problems are stated.