Problem

Source: Indonesian TST for IMO 2023 Stage 1: Test 1 - Algebra

Tags: algebra, polynomial, Polynomials, Integer Polynomial, integer polynomials, Indonesia, Indonesia TST



Find all Polynomial $P(x)$ and $Q(x)$ with Integer Coefficients satisfied the equation: \[Q(a+b) = \frac{P(a) - P(b)}{a - b}\]$\forall a, b \in \mathbb{Z}^+$ and $a>b$