Let n≥2 be a fixed integer and let ai,j(1≤i<j≤n) be some positive integers. For a sequence x1,...,xn of reals, let K(x1,....,xn) be the product of all expressions (xi−xj)ai,j where 1≤i<j≤n. Prove that if the inequality K(x1,....,xn)≥0 holds independently of the choice of the sequence x1,...,xn then all integers ai,j are even.