  For any prime $p$, let $y(p)$ denote the smallest integer $y$ such that every
reduced residue class $\pmod p$ is represented by the product of some subset of
$\{1,\dots,y\}$. It is easy to see that $y(p)$ is at least as large as the
smallest quadratic nonresidue $\pmod p$; we prove that $y(p) \ll_\varepsilon
p^{1/(4 \sqrt e)+\varepsilon}$, thus strengthening Burgess's classical result.
This result is of intermediate strength between two other results, namely
Burthe's proof that the multiplicative group $\pmod p$ is generated by the
integers up to $O_\varepsilon(p^{1/(4 \sqrt e)+\varepsilon}$, and Munsch and
Shparlinski's result that every reduced residue class $\pmod p$ is represented
by the product of some subset of the primes up to $O_\varepsilon(p^{1/(4 \sqrt
e)+\varepsilon}$. Unlike the latter result, our proof is elementary and similar
in structure to Burgess's proof for the least quadratic nonresidue.
