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OIMU 2007 Problem 5

    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

    Dataset text AI-MO AoPS. Quoted with source.

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