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 a1 < a2 < ... be an infinite sequence of positive integers and R(n) be the number of solutions of n = ai+aj. 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 sumKk = 1ck nrk, 1 > r1 > ... > rk > 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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