Question 162
Let $n \geq 3$ and $x_{1}, x_{2}, \ldots, x_{n}$ be $n$ distinct integers. Prove that
$$
\left(x_{1}-x_{2}\right)^{2}+\left(x_{2}-x_{3}\right)^{2}+\ldots+\left(x_{n}-x_{1}\right)^{2} \geq 4 n-6 .
$$
$$
\left(x_{1}-x_{2}\right)^{2}+\left(x_{2}-x_{3}\right)^{2}+\ldots+\left(x_{n}-x_{1}\right)^{2} \geq 4 n-6 .
$$