1) Show that if n is a positive integer and a and b are integers relatively prime to n such that = 1, then =
2) Let p be a prime divisor of the Fermat number
a) Show that
b) From part (a), conclude that , so that p must be of the form
1) Show that if n is a positive integer and a and b are integers relatively prime to n such that = 1, then =
2) Let p be a prime divisor of the Fermat number
a) Show that
b) From part (a), conclude that , so that p must be of the form
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