IMO 2006 Shortlist N4
Let P be a polynomial of degree n > 1 with integer coefficients and let k be any positive integer. Consider the polynomi...
Category: Number Theory
Problem
Let P be a polynomial of degree n > 1 with integer coefficients and let k be any positive integer. Consider the polynomial Q(x) = P(P(...P(P(x))...)), with k pairs of parentheses. Prove that Q has no more than n integer fixed points, i.e. integers satisfying the equation Q(x) = x. (Romania)