Modulo System

It is of common experience that railway time table is fixed with the prevision of 24 hours in a day and night. When we say that a particular train is arriving at 15 hours, it implies that the train will arrive at 3 p.m. according to our watch. Thus all the timing starting from 12 to 23 hours correspond to one of 0, 1, 3,…, 11 O’clock as indicated in watches. In other words all integers from 12 to 23 one equivalent to one or the other of integers 0, 1, 2, 3, …, 11 with modulo 12, in saying like this integers in question are divided into 12 classes.

In the manner described above the integer could be divided into 2 classes, or 5 classes or m (m being a positive integer) classes and then we would have written mod 2 or mod 5 or mod m. This system of representing integers is called modulo system.