Order and Primitive Roots

Let n be a positive integer and let gcd(a, n) = 1. The order of a mod n, denoted ordn(a), is the smallest positive integer m such that

am ≡ 1 (mod n). Example.

26 ≡ 1 (mod 9), 2i 6≡ 1 (mod 9) for 1 ≤ i ≤ 5, so ord9(2) = 6.