Question 91
Do there exist six pairwise distinct positive integers $a$, $b$, $c$, $d$, $e$ and $m$, such that
$$
\begin{cases}
a+b+c = d+e+m, \\
ab+bc+ac = de+em+dm, \\
abc = dem + 3^{2021} \cdot 2^{2022}?
\end{cases}
$$
(Igor Voronovich)
$$
\begin{cases}
a+b+c = d+e+m, \\
ab+bc+ac = de+em+dm, \\
abc = dem + 3^{2021} \cdot 2^{2022}?
\end{cases}
$$
(Igor Voronovich)