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**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 a_{1} \leq a_{2} \leq ... be an infinite sequence of integers for which all the sums a_{i}+a_{j}, 1 \leq i \leq j, are distinct. Then there are infinitely many integers k for which 2k can be represented in the form a_{i}+a_{j} but 2k+1 cannot be represented in this form. Several unsolved problems are stated.

**Classif.: ** * 11B13 Additive bases

00A07 Problem books

**Keywords: ** addition sequences; infinite sequence of integers; unsolved problems

**Citations: ** Zbl 569.10032; Zbl 588.10056

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