Question 20
Find all nonzero polynomials $P$ with real coefficients satisfying
$$P(P(k))=P(k)^2\quad\text{for }k=0,1,2,\ldots,(\deg P)^2.$$
$$P(P(k))=P(k)^2\quad\text{for }k=0,1,2,\ldots,(\deg P)^2.$$
MathNet 2011 Question 20
Math Olympiad Vault · MathNet 2011