Sonlu cisim
Bazı küçük sonlu cisimler > F25

F25, a + b√2 sayıları ile ifade edilir.
a ve b, tam sayı modül 5 dir.

2 + √2 kuvvetleri ile elde edilir.
| 0 | 1 | 2 | 3 | 4 |
| --- | --- | --- | --- | --- |
| ö (0) | ö (1) | ö (2) | ö (3) | ö (4) |
| 0 + 0√2 | 1 + 0√2 | 2 + 1√2 | 1 + 4√2 | 0 + 4√2 |
| ö (5) | ö (6) | ö (7) | ö (8) | ö (9) |
| 3 + 3√2 | 2 + 4√2 | 2 + 0√2 | 4 + 2√2 | 2 + 3√2 |
| ö (10) | ö (11) | ö (12) | ö (13) | ö (14) |
| 0 + 3√2 | 1 + 1√2 | 4 + 3√2 | 4 + 0√2 | 3 + 4√2 |
| ö (15) | ö (16) | ö (17) | ö (18) | ö (19) |
| 4 + 1√2 | 0 + 1√2 | 2 + 2√2 | 3 + 1√2 | 3 + 0√2 |
| ö (20) | ö (21) | ö (22) | ö (23) | ö (24) |
| 1 + 3√2 | 3 + 2√2 | 0 + 2√2 | 4 + 4√2 | 1 + 2√2 |
| + | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
| 0 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 1 | 1 | 7 | 18 | 6 | 3 | 12 | 14 | 19 | 22 | 5 | 20 | 2 | 10 | 0 | 23 | 16 | 11 | 21 | 15 | 13 | 9 | 8 | 24 | 4 | 17 |
| 2 | 2 | 18 | 8 | 19 | 7 | 4 | 13 | 15 | 20 | 23 | 6 | 21 | 3 | 11 | 0 | 24 | 17 | 12 | 22 | 16 | 14 | 10 | 9 | 1 | 5 |
| 3 | 3 | 6 | 19 | 9 | 20 | 8 | 5 | 14 | 16 | 21 | 24 | 7 | 22 | 4 | 12 | 0 | 1 | 18 | 13 | 23 | 17 | 15 | 11 | 10 | 2 |
| 4 | 4 | 3 | 7 | 20 | 10 | 21 | 9 | 6 | 15 | 17 | 22 | 1 | 8 | 23 | 5 | 13 | 0 | 2 | 19 | 14 | 24 | 18 | 16 | 12 | 11 |
| 5 | 5 | 12 | 4 | 8 | 21 | 11 | 22 | 10 | 7 | 16 | 18 | 23 | 2 | 9 | 24 | 6 | 14 | 0 | 3 | 20 | 15 | 1 | 19 | 17 | 13 |
| 6 | 6 | 14 | 13 | 5 | 9 | 22 | 12 | 23 | 11 | 8 | 17 | 19 | 24 | 3 | 10 | 1 | 7 | 15 | 0 | 4 | 21 | 16 | 2 | 20 | 18 |
| 7 | 7 | 19 | 15 | 14 | 6 | 10 | 23 | 13 | 24 | 12 | 9 | 18 | 20 | 1 | 4 | 11 | 2 | 8 | 16 | 0 | 5 | 22 | 17 | 3 | 21 |
| 8 | 8 | 22 | 20 | 16 | 15 | 7 | 11 | 24 | 14 | 1 | 13 | 10 | 19 | 21 | 2 | 5 | 12 | 3 | 9 | 17 | 0 | 6 | 23 | 18 | 4 |
| 9 | 9 | 5 | 23 | 21 | 17 | 16 | 8 | 12 | 1 | 15 | 2 | 14 | 11 | 20 | 22 | 3 | 6 | 13 | 4 | 10 | 18 | 0 | 7 | 24 | 19 |
| 10 | 10 | 20 | 6 | 24 | 22 | 18 | 17 | 9 | 13 | 2 | 16 | 3 | 15 | 12 | 21 | 23 | 4 | 7 | 14 | 5 | 11 | 19 | 0 | 8 | 1 |
| 11 | 11 | 2 | 21 | 7 | 1 | 23 | 19 | 18 | 10 | 14 | 3 | 17 | 4 | 16 | 13 | 22 | 24 | 5 | 8 | 15 | 6 | 12 | 20 | 0 | 9 |
| 12 | 12 | 10 | 3 | 22 | 8 | 2 | 24 | 20 | 19 | 11 | 15 | 4 | 18 | 5 | 17 | 14 | 23 | 1 | 6 | 9 | 16 | 7 | 13 | 21 | 0 |
| 13 | 13 | 0 | 11 | 4 | 23 | 9 | 3 | 1 | 21 | 20 | 12 | 16 | 5 | 19 | 6 | 18 | 15 | 24 | 2 | 7 | 10 | 17 | 8 | 14 | 22 |
| 14 | 14 | 23 | 0 | 12 | 5 | 24 | 10 | 4 | 2 | 22 | 21 | 13 | 17 | 6 | 20 | 7 | 19 | 16 | 1 | 3 | 8 | 11 | 18 | 9 | 15 |
| 15 | 15 | 16 | 24 | 0 | 13 | 6 | 1 | 11 | 5 | 3 | 23 | 22 | 14 | 18 | 7 | 21 | 8 | 20 | 17 | 2 | 4 | 9 | 12 | 19 | 10 |
| 16 | 16 | 11 | 17 | 1 | 0 | 14 | 7 | 2 | 12 | 6 | 4 | 24 | 23 | 15 | 19 | 8 | 22 | 9 | 21 | 18 | 3 | 5 | 10 | 13 | 20 |
| 17 | 17 | 21 | 12 | 18 | 2 | 0 | 15 | 8 | 3 | 13 | 7 | 5 | 1 | 24 | 16 | 20 | 9 | 23 | 10 | 22 | 19 | 4 | 6 | 11 | 14 |
| 18 | 18 | 15 | 22 | 13 | 19 | 3 | 0 | 16 | 9 | 4 | 14 | 8 | 6 | 2 | 1 | 17 | 21 | 10 | 24 | 11 | 23 | 20 | 5 | 7 | 12 |
| 19 | 19 | 13 | 16 | 23 | 14 | 20 | 4 | 0 | 17 | 10 | 5 | 15 | 9 | 7 | 3 | 2 | 18 | 22 | 11 | 1 | 12 | 24 | 21 | 6 | 8 |
| 20 | 20 | 9 | 14 | 17 | 24 | 15 | 21 | 5 | 0 | 18 | 11 | 6 | 16 | 10 | 8 | 4 | 3 | 19 | 23 | 12 | 2 | 13 | 1 | 22 | 7 |
| 21 | 21 | 8 | 10 | 15 | 18 | 1 | 16 | 22 | 6 | 0 | 19 | 12 | 7 | 17 | 11 | 9 | 5 | 4 | 20 | 24 | 13 | 3 | 14 | 2 | 23 |
| 22 | 22 | 24 | 9 | 11 | 16 | 19 | 2 | 17 | 23 | 7 | 0 | 20 | 13 | 8 | 18 | 12 | 10 | 6 | 5 | 21 | 1 | 14 | 4 | 15 | 3 |
| 23 | 23 | 4 | 1 | 10 | 12 | 17 | 20 | 3 | 18 | 24 | 8 | 0 | 21 | 14 | 9 | 19 | 13 | 11 | 7 | 6 | 22 | 2 | 15 | 5 | 16 |
| 24 | 24 | 17 | 5 | 2 | 11 | 13 | 18 | 21 | 4 | 19 | 1 | 9 | 0 | 22 | 15 | 10 | 20 | 14 | 12 | 8 | 7 | 23 | 3 | 16 | 6 |
| × | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- | --- |
0
| 1 | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 |
| 2 | 0 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 |
| 3 | 0 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 |
| 4 | 0 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 |
| 5 | 0 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 |
| 6 | 0 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 |
| 7 | 0 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 |
| 8 | 0 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
| 9 | 0 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| 10 | 0 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
| 11 | 0 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| 12 | 0 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 |
| 13 | 0 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 |
| 14 | 0 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 |
| 15 | 0 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 |
| 16 | 0 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
| 17 | 0 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| 18 | 0 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 |
| 19 | 0 | 19 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 |
| 20 | 0 | 20 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 |
| 21 | 0 | 21 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 |
| 22 | 0 | 22 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 |
| 23 | 0 | 23 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 |
| 24 | 0 | 24 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 |