MathDB

polynomial as sum of 3rd degree

Source: Baltic Way 2006

November 8, 2006

algebrapolynomialalgebra unsolved

Problem Statement

Prove that for every polynomial

P(x)

with real coefficients there exist a positive integer

m

and polynomials

P_{1}(x),\ldots , P_{m}(x)

with real coefficients such that

P(x) = (P_{1}(x))^{3}+\ldots +(P_{m}(x))^{3}