# Homework Help: Multiplicative Order

1. Aug 18, 2010

### hitmeoff

1. The problem statement, all variables and given/known data
Find all elements of Z*19 of multiplicative order 18.

2. Relevant equations
ak $$\equiv$$1 (mod n)

3. The attempt at a solution
So for a $$\in$$ Z*19 to have the multiplicative order 18 we have to satisfy the equivalence a18 $$\equiv$$ 1(mod 19), but the has to be a "smarter" way of calculating "a" than by just plug and chug numbers 1 through 18 to find the set thats equivalent to 1(mod 19)

2. Aug 18, 2010

anyone?