Modular arithmetic is a type of arithmetic on finite subsets of the natural numbers
For then
- iff
This is read as "a is congruent modulo n to b".
If then
If then
An easy way to calculate in mod{n} is they have the same remainder when divided by .
Congruence modulo n is an equivalence relation.
Let .
Then and so .
Thus .
Let such that .
Then .
Since .
Thus .
Let such that.
Then .
Then .
Thus and .