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Let f, g and a be polynomials with real coefficients, f and g in one variable and a in two variables. Suppose

f(x) - f(y) = a(x, y)(g(x) - g(y)) \forall x,y \in \mathbb{R}

Prove that there exists a polynomial h with f(x) = h(g(x)) \text{ } \forall x \in \mathbb{R}.

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