Let $n \ge 2$ be a fixed integer and let $a_{i,j} (1 \le i < j \le n)$ be some positive integers. For a sequence $x_1, ... , x_n$ of reals, let $K(x_1, .... , x_n)$ be the product of all expressions $(x_i - x_j)^{a_{i,j}}$ where $1 \le i < j \le n$. Prove that if the inequality $K(x_1, .... , x_n) \ge 0$ holds independently of the choice of the sequence $x_1, ... , x_n$ then all integers $a_{i,j}$ are even.