Let $\mathbb{F}$ be a finite field of $p$ elements, $\sigma \in \operatorname{Aut}(F)$ of order $m$, $\mathbb{F}^\sigma$ be the fixed field of $\sigma$, and $\mathbb{F}[x,\sigma]$ be a skew polynomial ring. A skew polynomial $f$ is central if $f\in \mathbb{F}^\sigma[x^m]$. Such elements generate two-sided ideals. A skew polynomial $g$ is a right divisor of $f$ if $f = hg$. My question is: how many right divisors does $f$ have?



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