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Laivirt algebra

Source: 2021 Korea Winter Program Test2 Day2 #7

February 17, 2021
algebrapolynomial

Problem Statement

Find all pair of constants (a,b)(a,b) such that there exists real-coefficient polynomial p(x)p(x) and q(x)q(x) that satisfies the condition below.
Condition: ∀x∈R,\forall x\in \mathbb R, p(x2)q(x+1)−p(x+1)q(x2)=x2+ax+bp(x^2)q(x+1)-p(x+1)q(x^2)=x^2+ax+b
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