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BALTIC-WAY 2005 Problem 4

  • Answer

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

Dataset text NuminaMath olympiads. Quoted with source.

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P(x)=x, P(x)=x^{2}+1, P(x)=x^{4}+2x^{2}+2

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