Hi again!

My problem is to show that a field of order $\displaystyle p^2$ exists for every prime p.

In an earlier problem I found that there were $\displaystyle p^2$monic quadratics in$\displaystyle Z_p[x]$, but I don't know if that's useful. I also showed that $\displaystyle (1/2)(p^2 + p)$ of those were factorable. Again, don't know if that's related at all but thought I'd throw it out there. Any ideas or theorems would be super helpful, thanks!