Question 148
Given three numbers $x$, $y$, $z$, and set $x_{1} = |x - y|$, $y_{1} = |y - z|$, $z_{1} = |z - x|$. From $x_{1}$, $y_{1}$, $z_{1}$, form in the same fashion the numbers $x_{2}$, $y_{2}$, $z_{2}$, and so on. It is known that $x_{n} = x$, $y_{n} = y$, $z_{n} = z$ for some $n$. Find all possible values of $(x, y, z)$.