MathDB

Let

f, g

and

a

be polynomials with real coefficients,

f

and

g

in one variable and

a

in two variables. Suppose f(x) \minus{} f(y) \equal{} a(x, y)(g(x) \minus{} g(y)) \forall x,y \in \mathbb{R} Prove that there exists a polynomial

h

with f(x) \equal{} h(g(x)) \text{ } \forall x \in \mathbb{R}.

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