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Find Polynomials

Source: Austrian-Polish 2006 Problem2

August 21, 2006
algebrapolynomialalgebra unsolved

Problem Statement

Find all polynomials P(x)P(x) with real coefficients satisfying the equation (x+1)3P(x−1)−(x−1)3P(x+1)=4(x2−1)P(x)(x+1)^{3}P(x-1)-(x-1)^{3}P(x+1)=4(x^{2}-1) P(x) for all real numbers xx.
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