MathDB
Complex polynomials composition

Source: IberoAmerican Olympiad For University Students

July 10, 2011
algebrapolynomialalgebra proposed

Problem Statement

Determine all pairs of polynomials f,g∈C[x]f,g\in\mathbb{C}[x] with complex coefficients such that the following equalities hold for all x∈Cx\in\mathbb{C}:
f(f(x))−g(g(x))=1+if(f(x))-g(g(x))=1+i f(g(x))−g(f(x))=1−if(g(x))-g(f(x))=1-i
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