**(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.