MathDB
f(x) = g(h(x)) - h(g(x)).

Source: 2021 Grand Duchy of Lithuania, Mathematical Contest p1 (Baltic Way TST) https://artofproblemsolving.com/community/c1321893_grand

October 30, 2021
algebrapolynomial

Problem Statement

Prove that for any polynomial f(x)f(x) (with real coefficients) there exist polynomials g(x)g(x) and h(x)h(x) (with real coefficients) such that f(x)=g(h(x))āˆ’h(g(x))f(x) = g(h(x)) - h(g(x)).
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