Prove that if and then the following are equivalent:
(a) which means is a generator of .
(b) i.e. and are relatively prime.
(c) such that .
If is a generator then the element can be written .
Assume . Then . Since divides the right side of the equation it has to divide both terms on the left, which is contradiction of .
for some . Then so any element can be written as a power of which means is a generator and therefore .