- Consider the powers of 3 (mod 7)
- 3
^{1}≡ 3, 3^{2}≡ 2, 3^{3}≡ 6, 3^{4}≡ 4, 3^{5}≡ 5, 3^{6}≡ 1 - Note that we obtain all nonzero congruence classes mod 7 as powers of 3
- Generally when p is a prime, a primitive root mod p is a number whose powers yield every nonzero class mod p
- Primitive Roots
- Let g be a primitive root for the prime p
- Let n be an integer. Then g
^{n}≡ 1 (mod p) if and only if n ≡ 0 (mod p - 1) - If j and k are integers, then g
^{j }≡ g^{j }(mod p) if and only if j ≡ k (mod p - 1)

## Tuesday, October 8, 2013

### Notes - Primitive Roots

The following are notes from Introduction to Cryptography with Coding Theory.

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