  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 $n$ can
be 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 both
properties. We answer this question in the affirmative. Our proof relies on a
deep result of Sawin on the $\mathbb{F}_q[t]$-analogue of Montgomery's
conjecture for convolutions of the von Mangoldt function.
