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Find all polynomials P such that P(P(P(x))) = Ax^n +19x+99

Source: Austrian Mathematical Olympiad 1999, Part 2, D2, P2

June 28, 2011
algebrapolynomialalgebra unsolved

Problem Statement

Given a real number AA and an integer nn with 2≤n≤192 \leq n \leq 19, find all polynomials P(x)P(x) with real coefficients such that P(P(P(x)))=Axn+19x+99P(P(P(x))) = Ax^n +19x+99.
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