For the first one...

(By the way Fermat's number is from the form: when

For your question now...

I don't use to work with notation, so...

, and

From which can be written as:

, we can deduce:

, and from , we get:

From your first theorem on this subject of orders... we can say that: , but , hence: ...

Similarly we can prove: .

Now, we have: and , hence: .

And the last part:

We have given that:

and ,

so: and from the theorem I mentioned before we get: , and with the (from the last part), we may deduce that