Multiplication Tables for the Group of Integers Modulo n

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Given a positive integer , the set
of positive integers coprime to
satisfies the axioms for an Abelian group under the operation of multiplication modulo
. For instance,
and
because
. This Demonstration shows the array plot of the multiplication table modulo
corresponding to
.
Contributed by: Jaime Rangel-Mondragon (August 2012)
Open content licensed under CC BY-NC-SA
Snapshots
Details
The order of is given by Euler's totient function
, implemented in Mathematica as EulerPhi[n], which for
has values
.
is cyclic only if
is
, or
, where
is an odd prime and
. The first few values for which
is not cyclic are
. Any generator in the cyclic case is called a primitive root modulo
.
Reference
[1] Wikipedia. "Multiplicative Group of Integers Modulo n." (Jul 31, 2012) en.wikipedia.org/wiki/Multiplicative_group_of _integers _modulo _n.
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