MathDB

5

Part of 2007 IberoAmerican Olympiad For University Students

Problems(1)

Complex polynomials composition

Source: IberoAmerican Olympiad For University Students

7/10/2011
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
algebrapolynomialalgebra proposed