An explicit representation as quasi-sum of squares of a polynomial generated by the AG inequality

Abstract

An explicit representation of the difference (x1+· · ·+xn)ⁿ−nⁿx1· · · xn for all natural n ≥ 2 is given as a sum of pij(xi − xj)2 over all 1 ≤ i < j n where pij = pij(x1, . . . , xn) are homogeneous polynomials of degree n − 2 whose coefficients at all possible monomials of degree n − 2 are positive.