华东师范大学学报(自然科学版) ›› 2004, Vol. 2004 ›› Issue (2): 1-4,23.

• 数学 统计学 •    下一篇

有限素域Fp上多项式xp-x-1的根的阶数

时俭益， 汪振华   

  1. 华东师范大学 网络信息安全研究所，上海 200062
  • 收稿日期:2002-04-10 修回日期:2003-06-27 出版日期:2004-06-25 发布日期:2004-06-25
  • 通讯作者: 时俭益

The Order of A Root of xp-x-1 over Fp

SHI Jian-yi, WANG Zhen-hua   

  1. Institute of Network Information Security, East China Normal University, Shanghai 200062, China
  • Received:2002-04-10 Revised:2003-06-27 Online:2004-06-25 Published:2004-06-25
  • Contact: SHI Jian-yi

摘要： 讨论了有限素域Fp上多项式xp-x-1的根αp的阶数o(αp)问题.文章猜测：等式o(αp)=mp:=（pp-1）/（p-1）对于任何素数p成立.文章通过具体例子介绍了在素数p给定的情形下证实该猜想的两种方法.

关键词: 多项式, 有限域, 根的阶数, 多项式, 有限域, 根的阶数

Abstract: The present paper is concerned with the order o(αp) of a root αp of the polynomial xp-x-1 over a prime field Fp. We propose a conjecture that o(αp)=mp:=(pp-1)/(p-1) for any prime p. Then we introduce two methods to verify the conjecture in certain cases.

Key words: finite field, order of a root, polynomial, finite field, order of a root

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