# Math Help - Irreducibility in Zp

1. ## Irreducibility in Zp

Show that there are infinitely many irreducible polynomials in Zp[x], where p is prime.

Deduce that there are infinitely many non-isomorphic finite fields of order a power of p.

2. Originally Posted by Mimi89
Mimick Euclides' proof for primes in $\mathbb{N}$: suppose $p_1(x),\ldots,p_n(x)$ are all the irreducible polynomials in $\mathbb{Z}_p[x]$ ,and define $p(x)=p_1(x)\cdot\ldots\cdot p_n(x)+1$ ...