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On an additive property of sequences of nonnegative integers

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Abstract

Let a1<a2<... be an infinite sequence of positive integers, let k≥2 be a fixed integer and denote by Rk(n) the number of solutions of n=ai1+ai2+...+aik. P. Erdős and A. Sárközy proved that if F(n) is a monotonic increasing arithmetic function with F(n)→+∞ and F(n)=o(n(log n)-2) then |R2(n)-F(n)| =o((F(n))1/2) cannot hold. The aim of this paper is to extend this result to k>2.

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REFERENCES

  1. P. ERDÖS and A. SáRKöZY, Problems and results on additive properties of general sequences, I, Pacific J. Math., 118 (1985), 347-357.

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  2. P. ERDÖS and A. SáRKöZY, Problems and results on additive properties of general sequences, II, Acta Math. Hungar., 48 (1986), 201-211.

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  1. Department of Algebra and Number Theory, Eötvös Loránd University, Pázmány Péter sétány 1/c, H-1117, Budapest, Hungary

    Gábor Horváth

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  1. Gábor Horváth
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Horváth, G. On an additive property of sequences of nonnegative integers. Periodica Mathematica Hungarica 45, 73–80 (2002). https://doi.org/10.1023/A:1022397913656

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  • DOI: https://doi.org/10.1023/A:1022397913656

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