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A set $S\subset \mathbb{N}$ is a Sidon set if all pairwise sums $s_1+s_2$(for $s_1, s_2\in S$, $s_1\leq s_2$) are distinct. A set $S\subset \mathbb{N}$is an asymptotic basis of order 3 if every sufficiently large integer $n$ canbe written as the sum of three elements of $S$. In 1993, Erd\H{o}s,S\'{a}rk\"{o}zy and S\'{o}s asked whether there exists a set $S$ with bothproperties. We answer this question in the affirmative. Our proof relies on adeep result of Sawin on the $\mathbb{F}_q[t]$-analogue of Montgomery'sconjecture for convolutions of the von Mangoldt function.

A solution to the Erd\H{o}s-S\'ark\"ozy-S\'os problem on asymptotic Sidon bases of order 3