For \(p\) a prime number, show that \(x^{p^n}-x \in \mathbb {F}_p[x]\) is the product of all irreducible polynomials of degree dividing \(n\) in \(\mathbb {F}_p[x]\).
Question
Math 6320 • Algebra II
Fall 2021 • Question 4
Question
Fall 2021 • Question 4
For \(p\) a prime number, show that \(x^{p^n}-x \in \mathbb {F}_p[x]\) is the product of all irreducible polynomials of degree dividing \(n\) in \(\mathbb {F}_p[x]\).