A new upper bound for finite additive bases

Details A new upper bound for finite additive bases A new upper bound for finite additive bases

2005-03-13

arxiv.org/abs/math/0503241v1

Mathematics

Number Theory

19 pages; LaTex

Scientific paper

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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