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P(x)-x|P^n(x)-x

Source: 2016 Thailand October Camp 2.5

February 26, 2022
polynomialalgebra

Problem Statement

Prove that for all polynomials P∈R[x]P \in \mathbb{R}[x] and positive integers nn, P(x)−xP(x)-x divides Pn(x)−xP^n(x)-x as polynomials.
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