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**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 569.10032

**Autor: ** Erdös, Paul; Sárközy, A.

**Title: ** Problems and results on additive properties of general sequences. I. (In English)

**Source: ** Pac. J. Math. 118, 347-357 (1985).

**Review: ** Let a_{1} < a_{2} < ... be an infinite sequence of positive integers and R(n) be the number of solutions of n = a_{i}+a_{j}. It is proved that, roughly speeking, R(n) cannot be approximated well by a monotonic increasing function. The results and proofs are of Erdös-Fuchs type [*P. Erdös* and *W. H. J. Fuchs*, J. Lond. Math. Soc. 31, 67-73 (1956; Zbl 070.04104)]. The special case when the approximating function has the shape **sum**^{K}_{k = 1}c_{k} n^{rk}, 1 > r_{1} > ... > r_{k} > 0 is due to *R. C. Vaughan* [J. Number Theory 4, 1-16 (1972; Zbl 226.10058)].

**Reviewer: ** A.Balog

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

00A07 Problem books

**Keywords: ** additive representations of integers; addition of sequences of integers; results of Erdös-Fuchs type; number of solutions

**Citations: ** Zbl 070.041; Zbl 226.10058

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