Question 8
Let $k$ be a positive integer. Find all polynomials
$$
P(x) = a_{0} + a_{1} x + \cdots + a_{n} x^{n}
$$
where the $a_{i}$ are real, which satisfy the equation
$$
P(P(x)) = [P(x)]^{k}
$$
$$
P(x) = a_{0} + a_{1} x + \cdots + a_{n} x^{n}
$$
where the $a_{i}$ are real, which satisfy the equation
$$
P(P(x)) = [P(x)]^{k}
$$