The digraphs of commutative rings under modular arithmetic reveal intriguing cycle patterns, many of which have yet to be explained. To help illuminate these patterns, we establish a set of new theorems. Rings with relatively prime moduli a and b are used to predict cycles in the digraph of the ring with modulus ab. Rings that use Pythagorean primes as their modulus are shown to always have a cycle in common. Rings with perfect square moduli have cycles that relate to their square root.
Dr. Bob Mallison
"New Theorems for the Digraphs of Commutative Rings,"
Rose-Hulman Undergraduate Mathematics Journal: Vol. 21
, Article 4.
Available at: https://scholar.rose-hulman.edu/rhumj/vol21/iss1/4