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素域Fp上多项式xp-x-a的阶

发表时间:2011-01-15  浏览量:1553  下载量:504
全部作者: 武跟强,李研超
作者单位: 兰州商学院信息工程学院;兰州商学院学生工作部
摘 要: 设p为一个素数、a为素域Fp中的一个元素,研究素域Fp上多项式xp-x-a的阶是否为pp-1,即xp-x-a是否为Fp上的本原多项式问题。根据对若干实例的分析,给出猜想:对任意素数p,xp-x-a为Fp上的本原多项式;从不同的角度进行分析,对此问题做较深入的讨论,并给出xp-x-a为Fp上本原多项式的几个充要条件及xp-x-a为Fp上本原多项式的一个作为充分条件的方程式。
关 键 词: 代数学;有限域;本原多项式;多项式的阶
Title: Order of polynomial xp-x-a over prime field Fp
Author: WU Genqiang, LI Yanchao
Organization: School of Information Engineering, Lanzhou University of Finance and Economics; Students’ Affairs Division, Lanzhou University of Finance and Economics
Abstract: Let p be a prime and a an element in prime field Fp. The order of the polynomial xp-x-a over Fp was treated. By the analyses of many special cases, a conjecture that the order of xp-x-a over Fp is pp-1, which is then a primitive polynomial over Fp, was proposed. From several different directions, this problem was analyzed and discussed deeply. Several necessary and sufficient conditions and a sufficient condition which is an equation were got to prove this conjecture.
Key words: algebra; finite fields; primitive polynomial; order of a polynomial
发表期数: 2011年1月第1期
引用格式: 武跟强,李研超. 素域Fp上多项式xp-x-a的阶[J]. 中国科技论文在线精品论文,2011,4(1):26-28.
 
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