Partitions of ${\mathbb{Z}}_n$ into Arithmetic Progressions

William Y. C. Chen, David G. L. Wang, Iris F. Zhang

We introduce the notion of arithmetic progression blocks or AP-blocks of ${\mathbb{Z}}_n$, which can be represented as sequences of the form $(x,x+m,x+2m,...,x+(i-1)m)(\mathrm{mod}n)$.…