8

Part of 1975 Canada National Olympiad

Problems(1)

Source:

k

be a positive integer. Find all polynomials P(x) \equal{} a_0 \plus{} a_1 x \plus{} \cdots \plus{} a_n x^n, where the

a_i

are real, which satisfy the equation P(P(x)) \equal{} \{ P(x) \}^k

algebrapolynomial