Multiplication Tables for the Group of Integers Modulo n

n

40

size

16

Given a positive integer

n

, the set

*



n

of positive integers coprime to

n

satisfies the axioms for an Abelian group under the operation of multiplication modulo

n

. For instance,

+



30

={1,7,11,13,17,19,23,29}

and

7*17=29

because

7×17=119≡29(mod30)

. This Demonstration shows the array plot of the multiplication table modulo

n

corresponding to

*



n

.