3

Part of 2009 Polish MO Finals

Problems(1)

polynomials P,Q,R are equal.

Source: Polish MO Round 3 2009,problem 3

P,Q,R

be polynomials of degree at least

1

with integer coefficients such that for any real number

x

holds: P(Q(x))\equal{}Q(R(x))\equal{}R(P(x)). Show that the polynomials

P,Q,R

algebrapolynomialalgebra unsolved