Modular Inverses

This is a visual map of multiplicative inverses modulo . The integers from to are placed clockwise on a circular number line with at the top. Two integers that are inverses modulo are connected by an arrow. An integer that is its own inverse is marked by a colored dot. Those integers that have no inverse modulo are not marked.

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DETAILS

Snapshot 1: for , all integers that have inverses are inverses of themselves
Snapshot 2: for some values of , the inverse map demonstrates four-fold rotational symmetry
Snapshot 3: for prime , all integers have inverses, so the map is much more detailed
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