# Congruence Modulo Integer/Examples

## Examples of Congruence Modulo an Integer

### Congruence Modulo $2$: $8 \equiv 2 \pmod 2$

$8 \equiv 2 \pmod 2$

### Congruence Modulo $2$: $8 \not \equiv 3 \pmod 2$

$8 \not \equiv 3 \pmod 2$

### Congruence Modulo $2$: $-3 \equiv -5 \pmod 2$

$-3 \equiv -5 \pmod 2$

### Congruence Modulo $3$: $12 \equiv 0 \pmod 3$

$12 \equiv 0 \pmod 3$

### Congruence Modulo $4$: $2 \equiv -6 \pmod 4$

$2 \equiv -6 \pmod 4$

### Congruence Modulo $4$: $3 \equiv 15 \pmod 4$

$3 \equiv 15 \pmod 4$

### Congruence Modulo $5$: $3 \equiv 18 \pmod 5$

$3 \equiv 18 \pmod 5$

### Congruence Modulo $5$: $13 \equiv 3 \pmod 5$

$13 \equiv 3 \pmod 5$

### Congruence Modulo $5$: $17 \equiv 12 \pmod 5$

$17 \equiv 12 \pmod 5$

### Congruence Modulo $6$: $-10 \equiv 8 \pmod 6$

$-10 \equiv 8 \pmod 6$

### Congruence Modulo $8$: $-2 \equiv 14 \pmod 8$

$-2 \equiv 14 \pmod 8$

### Congruence Modulo $12$: $11 \equiv -1 \pmod {12}$

$11 \equiv -1 \pmod {12}$

### Congruence Modulo $20$: $100 \equiv -40 \pmod {20}$

$100 \equiv -40 \pmod {20}$

### Congruence Modulo $12 \, 345 \, 678$: $12 \, 345 \, 678 \, 987 \, 654 \, 321 \not \equiv 0 \pmod {12 \, 345 \, 678}$

$12 \, 345 \, 678 \, 987 \, 654 \, 321 \not \equiv 0 \pmod {12 \, 345 \, 678}$

### Congruence Modulo $12 \, 345 \, 679$: $12 \, 345 \, 678 \, 987 \, 654 \, 321 \equiv 0 \pmod {12 \, 345 \, 679}$

$12 \, 345 \, 678 \, 987 \, 654 \, 321 \equiv 0 \pmod {12 \, 345 \, 679}$

### Congruence Modulo $4$: $57 \not \equiv 208 \pmod 4$

$57 \not \equiv 208 \pmod 4$

### Congruence Modulo $7561$: $531 \not \equiv 1236 \pmod {7561}$

$531 \not \equiv 1236 \pmod {7561}$

### Congruence Modulo $3$: $12321 \equiv 111 \pmod 3$

$12 \, 321 \equiv 111 \pmod 3$