Question 26
Find all positive integers $n$ such that there exists a polynomial $f$ of degree $n$ with integer coefficients and a positive leading coefficient and a polynomial $g$ with integer coefficients such that the equality
$$
xf^2(x) + f(x) = (x^3 - x)g^2(x)
$$
holds for every real $x$.
$$
xf^2(x) + f(x) = (x^3 - x)g^2(x)
$$
holds for every real $x$.