Problem

Source: Seniors Problem 10

Tags: inequalities, algebra unsolved, algebra



Let n2 be a fixed integer and let ai,j(1i<jn) be some positive integers. For a sequence x1,...,xn of reals, let K(x1,....,xn) be the product of all expressions (xixj)ai,j where 1i<jn. 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.