I'm my study of Galois theory I have been struggling with the following proposition without much success:
The polynomial $X^{p^n}-X$ is precisely the product of all the distinct irreducible polynomials in $\mathbb{F}_p[X]$ of degree $d$ where $d$ runs through all divisors of $n$
For example, $X^{p^6}-X$ is factorized by a polynomial of degree 1, 2, 3 and 6? It is posible to obtain them explicitly?