How would you find the possible orders of a(mod 29) if (a,29)=1?

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- August 4th 2009, 01:58 PMdiddledabble[SOLVED] Finding possible orders
How would you find the possible orders of a(mod 29) if (a,29)=1?

- August 4th 2009, 02:19 PMGamma
29 is prime, so every non identity element has order 29.

- August 4th 2009, 02:22 PMdiddledabbleWhat about composite numbers
Gamma,

What if the number was composite instead of a prime. Like 20? Then how would you find the order? - August 4th 2009, 02:32 PMGamma
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

or ).

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.