Let
![f, g](/media/m/6/c/9/6c9f0f573232fb12d5329f5899eba8aa.png)
and
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
be polynomials with real coefficients,
![f](/media/m/9/9/8/99891073047c7d6941fc8c6a39a75cf2.png)
and
![g](/media/m/9/5/8/958b2ae8c90cadb8c953ce50efb9c02a.png)
in one variable and
![a](/media/m/6/d/2/6d2832265560bb67cf117009608524f6.png)
in two variables. Suppose
Prove that there exists a polynomial
![h](/media/m/e/4/3/e438ac862510e579cf5cbdbe5904d4ba.png)
with
%V0
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 $f(x) = h(g(x)) \text{ } \forall x \in \mathbb{R}.$