Show that $3$ is a primitive root mod $14$. Then, write the other primitive roots mod $14$ in terms of powers of $3$. How many are there?
A bit lost with this question. Poked around online and found that:
Since we know $n= 14$ then the elements of $Z_n^×$ are the congruence classes $\{1, 3, 5, 9, 11, 13\}$; there are $\varphi(14) = 6$ of them. I also found a table of their powers mod $14$. Not really sure if this is going to be used for this problem though. Any hints/help is appreciated.
As it is a cyclic group of order $6$, if $g$ is a generator, the other generators are the $g^k$s with $k$ coprime to $6$, $1\le k\le6$, so there are two of them, $3$ and $3^5=3^{-1}=5$.