# Alg7.10

From Example Problems

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 .

Proof:

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 .