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TSTST 2014 Problem 3

  • Answer

Find all polynomials P(x)P(x) with real coefficients that satisfy P(x2)=P(x+1−x2)P(x \sqrt{2})=P\left(x+\sqrt{1-x^{2}}\right) for all real numbers xx with ∣x∣≤1|x| \leq 1.

Dataset text NuminaMath olympiads. Quoted with source.

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P(x)=f(U(x / \sqrt{2}))

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