MathDB

polynomial identity

Source: Russian Olympiad 2004, problem 11.3

May 4, 2004

algebrapolynomialcalculusRussia

Problem Statement

The polynomials

P(x)

and

Q(x)

are given. It is known that for a certain polynomial

R(x, y)

the identity P(x) \minus{} P(y) \equal{} R(x, y) (Q(x) \minus{} Q(y)) applies. Prove that there is a polynomial

S(x)

so that P(x) \equal{} S(Q(x)) \forall x.