Let , $\mathbb{F}_{p^{n}}$ is splitting field extension of the separable polynomial $x^{p^{n}}-x$ over $\mathbb{F}_{p}$. What should look like the extension with the generators and what will be the degree of extension?
I didn't understand how should I go ahead. First, the given polynomial is not irreducible.
What if I go for irreducible factor and then is it a cyclotomic polynomial always?
Euler function doesn't help much for finding the degree of that cyclotomic polynomial.
So, I got stuck totally.
What should I do?