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P(Q(x)) + P(R(x))=constant => P(x) or Q(x)+R(x) is constant

Source: International Zhautykov Olympiad 2012 - D1 - P3

January 31, 2012

algebrapolynomialalgebra unsolved

Problem Statement

Let

P, Q,R

be three polynomials with real coefficients such that

P(Q(x)) + P(R(x))=\text{constant}

for all

x

. Prove that

P(x)=\text{constant}

Q(x)+R(x)=\text{constant}

for all

x