Zentralblatt MATH

Publications of (and about) Paul Erdös

Zbl.No:  621.10041
Autor:  Erdös, Paul; Sárközy, A.
Title:  Problems and results on additive properties of general sequences. II. (In English)
Source:  Acta Math. Hung. 48, 201-211 (1986).
Review:  Let a1 < a2 < ... be an infinite sequence of positive integers and R(n) be the number of solutions of ai+aj = n. In part I [Pac. J. Math. 118, 347-357 (1985; Zbl 569.10032)] the authors proved that R(n) cannot be too regular in the sense R(n) = F(n)+o(\sqrt{F(n)}) cannot hold for "nice" functions F(n). In part II a probabilistic construction is presented to show that the above result is essentially best possible.
Reviewer:  A.Balog
Classif.:  * 11B13 Additive bases
                   11B83 Special sequences of integers and polynomials
                   11K65 Arithmetic functions (probabilistic number theory)
                   00A07 Problem books
Keywords:  additive representations of integers; infinite sequence; number of solutions
Citations:  Zbl 569.10032

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