Thread: Irreducible polynomials

Let F be a finite field. Show that F[x] has irreducible polynomials of arbitrarily high degree.

I am completely lost. Any help would be great. Thanks!

Originally Posted by page929

Let F be a finite field. Show that F[x] has irreducible polynomials of arbitrarily high degree.

I am completely lost. Any help would be great. Thanks!

In F[x] , irreducible polynomial = prime elements (why?), and then you can mimic Archimedes' proof of an infinite

number of prime numbers in the naturals.

Tonio