Find one primitive root of $\pmod{43^{63}}$. Also, is there a general formula for finding the primitive roots modulo an integer $n$?
In regards to the second question, if there is no general formula, then is there a proof that affirms this?
Here's what I done so far in regards to the specific question: It's possible that there's a primitive root since it is of the form $p^k$, but it might not have a primitive root. Apparently, $a$ is a primitive root modulo $n$ if and only if $\phi(n)$ (i.e. Euler's totient function) must be the multiplicative order of $a$, but this obviously doesn't even come close to simplifying this problem.
I strongly believe that there is no general formula for finding primitive roots. This should be obvious due to the "random" behaviour of numbers, though as for the proof, I am completely lost. It might be on Wikipedia or some advanced math website.
Edit: Initially I used $63^{43}$ but that clearly cannot have a primitive root since the set of integers coprime to it doesn't form a cyclic group. Also, according to Wikipedia, it seems like the number of primitive roots increases as the number increases, so I've changed the requirement to $1$ primitive root.