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AUSTRIAN-POLISH 1993 Problem 8

    Determine all real polynomials P(z)P(z) for which there exists a unique real polynomial Q(x)Q(x) satisfying the conditions Q(0)=0Q(0)= 0 , x+Q(y+P(x))=y+Q(x+P(y))x + Q(y + P(x))= y + Q(x + P(y)) for all x,y∈Rx,y \in R .

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