Multiplicative Order of 18 in Z*19

[hitmeoff]

Homework Statement

Find all elements of Z^*₁₉ of multiplicative order 18.

Homework Equations

a^k $$\equiv$$1 (mod n)

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 that's equivalent to 1(mod 19)

 

[hitmeoff]

anyone?