Degos's companion-matrix generation conjecture

Let $\mathbb{F}$ be a field of order $p$, where $p$ is prime. Let $g=X^n-1$, and let $f\in\mathbb{F}[X]$ be a primitive polynomial of degree $n$. For a polynomial $h\in\mathbb{F}[X]$, write $C_h$ for its companion matrix. Degos's conjecture.

$$\langle C_f,C_g\rangle=\operatorname{GL}_n(p).$$

The conjecture concerns generation of the general linear group by two companion matrices. The paper's abstract states that the conjecture is proved, so it is a theorem rather than an open problem.