The mod 12 clock: addition wraps around
Fermat's Little Theorem verification
a^(p−1) ≡ 1 (mod p) when p is prime, p∤a
Example p=5, a=2: 2⁴ = 16 = 3×5 + 1 ≡ 1 (mod 5) ✓
Example p=7, a=3: 3⁶ = 729 = 104×7 + 1 ≡ 1 (mod 7) ✓
Used in RSA encryption to prove decryption recovers the original message.
Addition table for ℤ/5ℤ (integers mod 5)
Every row and column contains {0,1,2,3,4} exactly once. The five elements form a closed group under addition mod 5. Red: sums that wrap around (≥5).
| + | 0 | 1 | 2 | 3 | 4 |
|---|---|---|---|---|---|
| 0 | 0 | 1 | 2 | 3 | 4 |
| 1 | 1 | 2 | 3 | 4 | 0 |
| 2 | 2 | 3 | 4 | 0 | 1 |
| 3 | 3 | 4 | 0 | 1 | 2 |
| 4 | 4 | 0 | 1 | 2 | 3 |
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