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AUSTRIAN-POLISH 2006 Problem 2

    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 .

    Dataset text AI-MO AoPS. Quoted with source.

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