MathDB

2024 Alg/NT Problem 10

Source:

April 14, 2024

algebra

Problem Statement

There exists a unique pair of polynomials

(P(x),Q(x))

such that \begin{align*} P(Q(x))&= P(x)(x^2-6x+7) \\ Q(P(x))&= Q(x)(x^2-3x-2) \end{align*} Compute

P(10)+Q(-10)

.
Proposed by Connor Gordon