Question 119
Find all real positive solutions (if any) to
$$
\begin{gathered}
x^{3}+y^{3}+z^{3}=x+y+z, \text{ and } \\
x^{2}+y^{2}+z^{2}=x y z .
\end{gathered}
$$
$$
\begin{gathered}
x^{3}+y^{3}+z^{3}=x+y+z, \text{ and } \\
x^{2}+y^{2}+z^{2}=x y z .
\end{gathered}
$$