Is 3 a primitive root of 11?
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 11 = 1 |
| 2 | 1 | 31 = 3 | 31 mod 11 = 3 |
| 3 | 2 | 32 = 9 | 32 mod 11 = 9 |
| 4 | 3 | 33 = 27 | 33 mod 11 = 5 |
| 5 | 4 | 34 = 81 | 34 mod 11 = 4 |
| 6 | 5 | 35 = 243 | 35 mod 11 = 1 |
| 7 | 6 | 36 = 729 | 36 mod 11 = 3 |
| 8 | 7 | 37 = 2187 | 37 mod 11 = 9 |
| 9 | 8 | 38 = 6561 | 38 mod 11 = 5 |
| 10 | 9 | 39 = 19683 | 39 mod 11 = 4 |
Final Evaluation:
3 is NOT a primitive root of 11
