Cycles of Sums of Integers

Bruno Dular

We study the period of the linear map $T:{\mathbb{Z}}_m^n\to {\mathbb{Z}}_m^n:(a_0,\dots ,a_{n-1})\mapsto (a_0+a_1,\dots ,a_{n-1}+a_0)$ as a function of $m$ and $n$, where $\mathb…