How would you find the possible orders of a(mod 29) if (a,29)=1?
Do you know the definition of order of an element ? In additive notation it is the smallest positive integer n such that (mod n). You just gotta calculate man, it is just a lot easier when n is prime because by definition of prime
Thus if (mod p), then , so if
(mod p) then you are talking about the identity element so it has order 1, if then clearly the order is p, because and p cannot divide anything smaller than p itself.