I'm reading through some notes online concerning finite fields, and attempting to come up with a proof that all finite fields of the same size are isomorphic. But I'm getting stuck at a certain point, and I was wondering of you might have any hints.
If $F$ is any field with $p^d$ elements and $m(x)$ has coefficients all from $\mathbb{F}_p$ and is an irreducible polynomial of degree $d$ over $\mathbb{F}_p$, then $m(x)$ has roots in $F$. Is this immediately obvious? It seems to be stated so but I can't see why.