Let f(x) be a polynomial with rational coefficients and α be a real number such that \alpha^3 \minus{} \alpha \equal{} [f(\alpha)]^3 \minus{} f(\alpha) \equal{} 33^{1992}. Prove that for each n≥1, \left [ f^{n}(\alpha) \right]^3 \minus{} f^{n}(\alpha) \equal{} 33^{1992}, where f^{n}(x) \equal{} f(f(\cdots f(x))), and n is a positive integer. algebrapolynomialfunctional equationIterationIMO ShortlistIMO Longlist