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:结合两个基本证据,我们用0.2 $来缩小上下下界限之间的差距。 在经典组合数字理论问题中,我们用0.2 $来缩小上下界限之间的差距。我们显示,Sidon的Sidon系列最大规模为 1, 2,\ ldots, n ⁇ $最多为$\sqrt{n ⁇ 0.998n ⁇ 1/4}$, 足够大。