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Modular arithmetic

From Wikiversity

Modular arithmetic is a type of arithmetic on finite subsets of the natural numbers

Definition

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For then

iff

This is read as "a is congruent modulo n to b".

Examples

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If then

If then

Calculation

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An easy way to calculate in mod{n} is they have the same remainder when divided by .

Equivalence

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Congruence modulo n is an equivalence relation.

Reflexivity

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Let . Then and so . Thus .

Symetry

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Let such that . Then . Since . Thus .

Transitivity

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Let such that. Then . Then . Thus and .