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AUSTRIAN-POLISH 1995 Problem 4

    Determine all polynomials P(x)P(x) with real coefficients such that P(x)2+P(1x)2=P(x2)P(1x2)P(x)^2 + P\left(\frac{1}{x}\right)^2= P(x^2)P\left(\frac{1}{x^2}\right) for all xx .

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