Congruence Modulo Integer/Examples
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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 $3$: $12321 \equiv 111 \pmod 3$
- $12 \, 321 \equiv 111 \pmod 3$