Question 170
Solve in real numbers the system of equations
$$
\begin{gathered}
x_{1}\left(x_{1}-1\right)=x_{2}-1 \\
x_{2}\left(x_{2}-1\right)=x_{3}-1 \\
\cdots \\
x_{2016}\left(x_{2016}-1\right)=x_{2017}-1 \\
x_{2017}\left(x_{2017}-1\right)=x_{1}-1 .
\end{gathered}
$$
$$
\begin{gathered}
x_{1}\left(x_{1}-1\right)=x_{2}-1 \\
x_{2}\left(x_{2}-1\right)=x_{3}-1 \\
\cdots \\
x_{2016}\left(x_{2016}-1\right)=x_{2017}-1 \\
x_{2017}\left(x_{2017}-1\right)=x_{1}-1 .
\end{gathered}
$$