Primitive Root Modular Arithmetic Question 3)Given a prime $p$ and an integer $a$, we say that $a$ is a $\textit{primitive root} \pmod p$ if the set $\{a,a^2,a^3,\ldots,a^{p-1}\}$ contains exactly one element congruent to each of $1,2,3,\ldots,p-1\pmod p$.
For example, $2$ is a primitive root $\pmod 5$ because $\{2,2^2,2^3,2^4\}\equiv \{2,4,3,1\}\pmod 5$, and this list contains every residue from $1$ to $4$ exactly once.
However, $4$ is not a primitive root $\pmod 5$ because $\{4,4^2,4^3,4^4\}\equiv\{4,1,4,1\}\pmod 5$, and this list does not contain every residue from $1$ to $4$ exactly once.
What is the sum of all integers in the set $\{1,2,3,4,5,6\}$ that are primitive roots $\pmod 7$?
I have no clue how to answer this question. Any help will be great. 
Thank you very much.

Modulo $7$, the powers of $1$ are $1,1,1,1,1,1,$ so $1$ is not a primitive root; the powers of $2$ are $2,4,1,2,4,1,$ so $2$ is not a primitive root; and the powers of $3$ are $3,2,6,4,5,1$, so $3$ is a primitive root.  Can you take it from here?  Test whether $4,5,$ and $6$ are primitive roots, and then compute the sum of the primitive roots as requested.  
