(a) I want to use a result known as the "Subfield Test", but unfortunately I don't see how to make use of the fact that in order to simplify things.
To use the Subfield Test I must show that for any in K, and belong to .
Let , so by definition and . But how do we deduce that ( or ?
The only thing we are told is the characteristic of F is a prime (which is the least positive integer p such that px=0 for all x in F). Is there any way we can somehow use Fermat's little theorem?
(b) Any clues to get me started is really appreciated.