Let $n \ge 5$ be an integer and let $x_1, x_2, ... , x_n$ be $n$ distinct integer numbers such that no $3$ of them can be in arithmetic progression. Prove that if for all $1 \le i, j \le n$ we have $$2|x_i - x_j | \le n(n - 1)$$then there exist $4$ distinct indices $i, j, k, l \in \{1, 2, ... , n\}$ such that $$x_i + x_j = x_k + x_l.$$