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Polynomial induction, Serbia additional TST 2016

Source: Serbia additional TST 2016

April 5, 2016
algebrapolynomialPolynomials

Problem Statement

Let P0(x)=x3−4xP_0(x)=x^3-4x. Sequence of polynomials is defined as following:\\ Pn+1=Pn(1+x)Pn(1−x)−1P_{n+1}=P_n(1+x)P_n(1-x)-1.\\ Prove that x2016∣P2016(x)x^{2016}|P_{2016}(x).
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