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x + Q(y + P(x))= y + Q(x + P(y)) when Q(0)= 0

Source: Austrian - Polish 1993 APMC

May 3, 2020
polynomialfunctionalfunctional equationalgebra

Problem Statement

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,yāˆˆRx,y \in R.
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