A field with $p^n$ elements is a splitting field of $x^{p^n}

The field with $p^n$ elements consists exactly of the roots of $x^{p^n}-x$.Suggest a slogan

Let $p$ be a prime, let $n \geq 1$, and let $F$ be a field with $p^n$ elements, whose prime subfield is $\FF_p$. Then $F$ is a splitting field of $\rho(x) = x^{p^n} - x$ over $\FF_p$, and the elements of $F$ are exactly the $p^n$ roots of $\rho$ in $F$.