Polynomials of maximal period over primary residue rings

The maximality criterion for the period of a polynomial over primary residue ring is proved. This criterion generalize the results of the paper [1], where the case of polynomials over $\mathbb Z_{2^n}$ was considered, to the case of arbitrary primary ring $\mathbb Z_{p^n}$. The criterion is based on the concept of “marked polynomial” introduced in [1] and allows to verify the maximality of the period of a polynomial using only its coefficients. Some sufficient conditions of maximality of the period of a polynomial over $\mathbb Z_{p^n}$ are given.