Field of Order p^2 Exists for Every Prime p

[kimberu]

Homework Statement

Show that a field of order p² exists for every prime p.

The Attempt at a Solution

In an earlier problem I found that there were p² monic quadratics in Z_p[x], but I don't know if that's useful. Any ideas or theorems would be super helpful, thanks!

 

[ABarrios]

This is an application of the Frobenius endomorphism if I am not mistaken,

http://en.wikipedia.org/wiki/Frobenius_endomorphism