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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