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In this entry point into the subject, combining two elementary proofs, wedecrease the gap between the upper and lower bounds by $0.2\%$ in a classicalcombinatorial number theory problem. We show that the maximum size of a Sidonset of $\{ 1, 2, \ldots, n\}$ is at most $\sqrt{n}+ 0.998n^{1/4}$ forsufficiently large $n$.

An upper bound on the size of Sidon sets