An upper bound on the size of Sidon sets

Abstract

In this entry point into the subject, combining two elementary proofs, we decrease the gap between the upper and lower bounds by $0.2\%$ in a classical combinatorial number theory problem. We show that the maximum size of a Sidon set of $\{1,2,\dots ,n\}$ is at most $\sqrt{n}+0.998n^{1/4}$ for sufficiently large $n$.

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