Journal of Shanghai University(Natural Science Edition) ›› 2020, Vol. 26 ›› Issue (2): 189-196.doi: 10.12066/j.issn.1007-2861.2026

• Research Articles • Previous Articles     Next Articles

Factorization of xn-1 over finite field Fp

DING Yang(), WANG Yongchao   

  1. College of Sciences, Shanghai University, Shanghai 200444, China
  • Received:2018-04-04 Online:2020-04-30 Published:2020-04-29
  • Contact: DING Yang E-mail:dingyang@shu.edu.cn

Abstract:

Let p be an odd prime number. This paper presents an algorithm for the factorization of xn-1 over prime field Fp, where n=d(p+1), d|(p-1) and dp-1. As is suggested, the factorization problem can be solved by Dickson polynomials based on a primitive polynomial over Fp. Some examples are provided for the explanation of this algorithm.

Key words: Dickson polynomials, primitive polynomials, factorization of polynomial

CLC Number: