MathDB

Prove that P(x,y) cannot be factorised -[VMO 2011]

Source:

January 12, 2011

algebrapolynomialalgebra proposed

Problem Statement

Let

n\in\mathbb N

and define

P(x,y)=x^n+xy+y^n.

Show that we cannot obtain two non-constant polynomials

G(x,y)

and

H(x,y)

with real coefficients such that

P(x,y)=G(x,y)\cdot H(x,y).