Modular arithmetic is a type of arithmetic on finite subsets of the natural numbers
Definition[edit]
For
then
iff 
This is read as "a is congruent modulo n to b".
Examples[edit]
If
then



If
then


Calculation[edit]
An easy way to calculate in mod{n} is
they have the same remainder when divided by
.
Equivalence[edit]
Congruence modulo n is an equivalence relation.
Reflexivity[edit]
Let
.
Then
and
so
.
Thus
.
Symetry[edit]
Let
such that
.
Then
.
Since
.
Thus
.
Transitivity[edit]
Let
such that
.
Then
.
Then
.
Thus
and
.