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 $\{ 1, 2, \ldots, n\}$ is at most $\sqrt{n}+ 0.998n^{1/4}$ for sufficiently large $n$.

翻译：在主题的这一切入点,结合两个基本证据,在经典组合数字理论问题中,我们将上下界限之间的差额减少0.2美元。我们表明,Sidon系列的最大价值为1,2,\ldots,n ⁇ $最多为$\sqrt{n ⁇ 0.998n ⁇ 1/4}美元,数额足够大。