Question 175
Determine positive integers $x$, $y$, $z$ which satisfy the system
$$
\begin{aligned}
x + y + z &= xy + yz + zx \\
xyz &= 1
\end{aligned}
$$
and have the least possible sum.
$$
\begin{aligned}
x + y + z &= xy + yz + zx \\
xyz &= 1
\end{aligned}
$$
and have the least possible sum.