is there an easy way to find primitive roots for a specific mod?
There isn't a specific formula to find primitive roots. However, say that you have found one primitive root, modulo . Then, is also a primitive root iff and this gives the complete list.
More here: How to find a primitive root of N
So say I have found a primitive root mod 29. namely 2.
then the other primitive roots mod 29 are powers of 2?
that means that 8 is also a primitive root because 2^3=8 and (28,3)=1.
but 2^5=32 (28,5)=1 does that mean that 3 is a primitive root because 32 mod 29 is congruent to 3?
is the only other primitive root for 29 8?