IMO 2006, Problem 5

[Marco]

Let $ P(x) $ be a polynomial of degree $ n > 1 $ with integer coefficients and let $ k $ be a positive integer. Consider the polynomial $ Q(x) = P(P( \cdots P(P(x)) \cdots )) $, where $ P $ occurs $ k $ times. Prove that there are at most $ n $ integers $ t $ such that $ Q(t) = t $.

[MindFlyer]

Penso che sia da classificare come Algebra.
Sposto il thread.