Modular Inverses

modulus

120

This is a visual map of multiplicative inverses modulo

n

. The integers from

0

to

n-1

are placed clockwise on a circular number line with

0

at the top. Two integers that are inverses modulo

n

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

n

are not marked.

Snapshot 1: for

n=24

, all integers that have inverses are inverses of themselves

Snapshot 2: for some values of

n

, the inverse map demonstrates four-fold rotational symmetry

Snapshot 3: for prime

n

, all integers have inverses, so the map is much more detailed

Aaron Dunigan AtLee