Number Theory/Powers modulo 19
The following table shows the powers of integers modulo 19.
| x | x2 | x3 | x4 | x5 | x6 | x7 | x8 | x9 | x10 | x11 | x12 | x13 | x14 | x15 | x16 | x17 | x18 |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 | 1 |
| 2 | 4 | 8 | 16 | 13 | 7 | 14 | 9 | 18 | 17 | 15 | 11 | 3 | 6 | 12 | 5 | 10 | 1 |
| 3 | 9 | 8 | 5 | 15 | 7 | 2 | 6 | 18 | 16 | 10 | 11 | 14 | 4 | 12 | 17 | 13 | 1 |
| 4 | 16 | 7 | 9 | 17 | 11 | 6 | 5 | 1 | 4 | 16 | 7 | 9 | 17 | 11 | 6 | 5 | 1 |
| 5 | 6 | 11 | 17 | 9 | 7 | 16 | 4 | 1 | 5 | 6 | 11 | 17 | 9 | 7 | 16 | 4 | 1 |
| 6 | 17 | 7 | 4 | 5 | 11 | 9 | 16 | 1 | 6 | 17 | 7 | 4 | 5 | 11 | 9 | 16 | 1 |
| 7 | 11 | 1 | 7 | 11 | 1 | 7 | 11 | 1 | 7 | 11 | 1 | 7 | 11 | 1 | 7 | 11 | 1 |
| 8 | 7 | 18 | 11 | 12 | 1 | 8 | 7 | 18 | 11 | 12 | 1 | 8 | 7 | 18 | 11 | 12 | 1 |
| 9 | 5 | 7 | 6 | 16 | 11 | 4 | 17 | 1 | 9 | 5 | 7 | 6 | 16 | 11 | 4 | 17 | 1 |
| 10 | 5 | 12 | 6 | 3 | 11 | 15 | 17 | 18 | 9 | 14 | 7 | 13 | 16 | 8 | 4 | 2 | 1 |
| 11 | 7 | 1 | 11 | 7 | 1 | 11 | 7 | 1 | 11 | 7 | 1 | 11 | 7 | 1 | 11 | 7 | 1 |
| 12 | 11 | 18 | 7 | 8 | 1 | 12 | 11 | 18 | 7 | 8 | 1 | 12 | 11 | 18 | 7 | 8 | 1 |
| 13 | 17 | 12 | 4 | 14 | 11 | 10 | 16 | 18 | 6 | 2 | 7 | 15 | 5 | 8 | 9 | 3 | 1 |
| 14 | 6 | 8 | 17 | 10 | 7 | 3 | 4 | 18 | 5 | 13 | 11 | 2 | 9 | 12 | 16 | 15 | 1 |
| 15 | 16 | 12 | 9 | 2 | 11 | 13 | 5 | 18 | 4 | 3 | 7 | 10 | 17 | 8 | 6 | 14 | 1 |
| 16 | 9 | 11 | 5 | 4 | 7 | 17 | 6 | 1 | 16 | 9 | 11 | 5 | 4 | 7 | 17 | 6 | 1 |
| 17 | 4 | 11 | 16 | 6 | 7 | 5 | 9 | 1 | 17 | 4 | 11 | 16 | 6 | 7 | 5 | 9 | 1 |
| 18 | 1 | 18 | 1 | 18 | 1 | 18 | 1 | 18 | 1 | 18 | 1 | 18 | 1 | 18 | 1 | 18 | 1 |