Congruence Modulo Integer/Examples/12,345,678,987,654,321 equiv 0 mod 12,345,679

Example of Congruence Modulo an Integer

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

Proof
By definition of congruence:
 * $x \equiv y \pmod n$ $x - y = k n$

for some $k \in \Z$.

We have:
 * $12 \, 345 \, 678 \, 987 \, 654 \, 321 - 0 = 12 \, 345 \, 678 \, 987 \, 654 \, 321 = 999 \, 999 \, 999 \times 12 \, 345 \, 679$

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