Is 3 a primitive root of 7?
If p is prime, then b is a primitive root if
Powers of b include all residue classes mod p
Primitive Root Table:
| n | n - 1 | bn - 1 | bn - 1 mod p |
|---|---|---|---|
| 1 | 0 | 30 = 1 | 30 mod 7 = 1 |
| 2 | 1 | 31 = 3 | 31 mod 7 = 3 |
| 3 | 2 | 32 = 9 | 32 mod 7 = 2 |
| 4 | 3 | 33 = 27 | 33 mod 7 = 6 |
| 5 | 4 | 34 = 81 | 34 mod 7 = 4 |
| 6 | 5 | 35 = 243 | 35 mod 7 = 5 |
Final Evaluation:
3 is a primitive root of 7
