If $f$ is irreducible over $\mathbb{F}_p[x]$ of degree $d$, then
$$g(x)^{p^d} \equiv g(x) \bmod f(x)$$ and $p^d - 1$ is the order of the cyclic group $\left( \mathbb{F}_p[x]/f(x) \right)^{\times}$. Is there a multivariate version of this?
2026-03-30 12:57:39.1774875459
Multivaritate version of Fermat's little theorem
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