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Polynomial f s.t. f(x)|f(x^2-1) - OIMU 2008 Problem 2

Source:

August 28, 2010
algebrapolynomialratiogeometryalgebra proposed

Problem Statement

Prove that for each natural number nn there is a polynomial ff with real coefficients and degree nn such that p(x)=f(x2āˆ’1) p(x)=f(x^2-1) is divisible by f(x)f(x) over the ring R[x]\mathbb{R}[x].
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