FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1995, VOLUME 1, NUMBER 2, PAGES 549-551

Polynomials of maximal period over primary residue rings

A.S.Kuzmin

The maximality criterion for the period of a polynomial over primary residue ring is proved. This criterion generalize the results of A.A.Nechaev, 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 by A.A.Nechaev 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.

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