I'm currently studying Number Theory and I've stumbled upon a question where I need to: Find the sum of all products of pairs of distinct primitive roots mod 83.
Solving attempt: I've tried to find all the primitive roots mod 83 but then I realized that there are probably many of them and the calculations are getting heavy on high powers. I guess there might be a simpler approach then just finding all the primitive roots and summing all the products of distinct primitive roots. I do know that the product of all primitive roots (mod p) is 1 mod p but I don't see how it helps me.
Any help would be appreciated.