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I know how to do it with smaller numbers by testing,but here we have φ(φ(41))=16 solutions out of 40 possibilities.I think I somehow have to use indices. Actually how do I even find 1 primitive root?Should I just pick a random number and test? Any help will be appreciated.

Bill Dubuque
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Alex Brown
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    Start systematically with $2,3,\ldots$. Then you'll see that there are $16$ primitive roots modulo $41$ which are $$6,7,11,12,13,15,17,19,22,24,26,28,29,30,34,35$$ A more general way (there is no good way in general) can be found in this duplicate: "There is no general formula to find a primitive root. Typically, what you do is you pick a number and test. Once you find one primitive root, you find all the others." – Dietrich Burde May 15 '23 at 14:24

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