IMO 2009 Shortlist N5

Let P(x) be a non-constant polynomial with integer coefficients. Prove that there is no function T from the set of integ...

IMO 2009 Shortlist N5

Category: Number Theory

Problem

Let P(x) be a non-constant polynomial with integer coefficients. Prove that there is no function T from the set of integers into the set of integers such that the number of integers x with Tn (x) = x is equal to P(n) for every n ≥ 1, where Tn denotes the n-fold application of T.