The concept of **numerical congruence** was formulated by Gauss.
If two numbers have the same remainder when divided by a given number `m`
(called the *modulus*),
then they are said to be **congruent modulo m**. We say "

Modular arithmetic is occasionally referred to as "clock arithmetic." If it is 11:00 right now, two hours later it will be 1:00, and 12 hours later it will be 11:00 again. Adding and subtracting time on a clock is quite similar to modular arithmetic modulo 12, although in modular arithmetic the numbers would range from 0 to 11, not 1 to 12.

Here is a sample of recreational applications of congruences:

There is also a congruences worksheet available.