An example of this is the clock which starts repeating itself when it has reached 12. Therefore it is said that the clock follows an arithmetic modulo 12.
Ex: If you add 7 hours to 8 o’clock the result is not 15 since when thee clock reaches zero it starts over from zero once again so the result is 7+8=3 in this arithmetic.
For a positive integer n, two integers a and b are said to be congruent modulo n,
if the the remainder is the same when a and b are divided by n.
if their difference a − b is an integer multiple of n. The number n is called the modulus of the congruence.
- e.g. 14
14≡12 (mod 2)
An example of an application of this mathematical tool is the Chinese Remainder Theorem.