An n-quadratic equation
Source: Brazilian Math Olympiad 2007, Problem 1
November 2, 2007
quadraticsinductionalgebrapolynomiallimitquadratic formula
Problem Statement
Let f(x) \equal{} x^2 \plus{} 2007x \plus{} 1. Prove that for every positive integer , the equation \underbrace{f(f(\ldots(f}_{n\ {\rm times}}(x))\ldots)) \equal{} 0 has at least one real solution.