Ducci on ${\mathbb{Z}}_m^3$ and the Max Period

Mark L. Lewis, Shannon M Tefft

Let $D(x_1,x_2,...,x_n)=(x_1+x_2\text{mod}m,x_2+x_3\text{mod}m,...,x_n+x_1\text{mod}m)$ where $D\in End({\mathbb{Z}}_m^n)$ be the Ducci function. The se…