Question

Difference between modular arithmetic and ordinary arithmetic

Answer 1

In ordinary arithmetic the resulting value will be from an infinite set of values whereas in modular arithmetic, the resulting value will be from a finite set of values.

Example :

Lets take addition of two numbers.

In ordinary arithmetic the sum of two numbers will be an integer in the range of :

(...., - 3, - 2, - 1, 0 , 1, 2, 3, .....)

In modular arithmetic the sum of two integers say (x + y) mod n will be in the range :

(0, 1, 2,... n-1)