Modular Multiplication

Modular arithmetic is a system arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. This becomes very useful when working with prime numbers.

This app that allows the user to select a number n less than 53 that is not a prime and displays a multiplication table for all the elements [q]n ∈ Zn where gcd(q, n) = 1. It also counts the number of elements of each order and displays the results in a graph.

General notation: [a]n means a mod n in Zn.

Important properties of Zn arithmetic:

• [a + b]n = [a]n + [b]n

• [ab]n = [a]n[b]n

• If n is composite, then Z+n and Z⇥n are not groups.

• If n is prime, then Z+n and Z⇥n are groups.

Check out the app at this site.