Modular arithmetic

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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 .