Question 141
Given four numbers $x, y, z, t$, let $(a, b, c, d)$ be a permutation of $(x, y, z, t)$ and set $x_{1}=|a-b|$, $y_{1}=|b-c|$, $z_{1}=|c-d|$, and $t_{1}=|d-a|$. From $x_{1}, y_{1}, z_{1}, t_{1}$, form in the same fashion the numbers $x_{2}, y_{2}, z_{2}, t_{2}$, and so on. It is known that $x_{n}=x$, $y_{n}=y$, $z_{n}=z$, $t_{n}=t$ for some $n$.
Find all possible values of $(x, y, z, t)$.
Find all possible values of $(x, y, z, t)$.