Question 125
Find all triples $(x; y; z)$ of real numbers satisfying the system
$$
\begin{cases} (x+1)(x^2+1) = y^3+1, \\ (y+1)(y^2+1) = z^3+1, \\ (z+1)(z^2+1) = x^3+1. \end{cases}
$$
$$
\begin{cases} (x+1)(x^2+1) = y^3+1, \\ (y+1)(y^2+1) = z^3+1, \\ (z+1)(z^2+1) = x^3+1. \end{cases}
$$