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A new upper bound for finite additive bases

Sinan Gunturk·Melvyn B. Nathanson
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Abstract

Let n(2,k) denote the largest integer n for which there exists a set A of k nonnegative integers such that the sumset 2A contains {0,1,2,...,n-1}. A classical problem in additive number theory is to find an upper bound for n(2,k). In this paper it is proved that limsup_{k\to\infty} n(2,k)/k^2 \leq 0.4789.

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Sinan Gunturk, Melvyn B. Nathanson. 2005-03-13. A new upper bound for finite additive bases. https://arxiv.org/abs/math/0503241

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