设Fq为有限域,文献(P.P.Wang,et al.Finite Fields and Their Applications,2012,18(4):800-813.)给出了特征为2的有限域F_q中存在α∈F_q使得α和α+α^(-1)都是F_q中本原元的几个充分条件,随后,文献(Q.Y.Liao,et al.Chin Annals Math,...设Fq为有限域,文献(P.P.Wang,et al.Finite Fields and Their Applications,2012,18(4):800-813.)给出了特征为2的有限域F_q中存在α∈F_q使得α和α+α^(-1)都是F_q中本原元的几个充分条件,随后,文献(Q.Y.Liao,et al.Chin Annals Math,2015,in press.)将其结果推广到任意特征的有限域上.讨论任意特征的有限域F_q中存在2个本原元α,β,使得α+β亦为本原元的几个充分条件,进而,利用特征和的方法得到一个满足此条件的q的下界q_0=4.98×10^(86).最后,利用计算机验证了特征为2的有限域除F2与F4外均满足此条件.展开更多
Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q^n) such that α + α^(-1)is also ...Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q^n) such that α + α^(-1)is also primitive or α + α^(-1)is primitive and α is a normal element of F_(q^n) over F_q.展开更多
文摘设Fq为有限域,文献(P.P.Wang,et al.Finite Fields and Their Applications,2012,18(4):800-813.)给出了特征为2的有限域F_q中存在α∈F_q使得α和α+α^(-1)都是F_q中本原元的几个充分条件,随后,文献(Q.Y.Liao,et al.Chin Annals Math,2015,in press.)将其结果推广到任意特征的有限域上.讨论任意特征的有限域F_q中存在2个本原元α,β,使得α+β亦为本原元的几个充分条件,进而,利用特征和的方法得到一个满足此条件的q的下界q_0=4.98×10^(86).最后,利用计算机验证了特征为2的有限域除F2与F4外均满足此条件.
基金supported by the National Natural Science Foundation of China(No.11401408)the Natural Science Foundation of Sichuan Province(No.14ZA0034)+2 种基金the Sichuan Normal University Key Project Foundation(No.13ZDL06)supported by the National Natural Science Foundation of China(No.11001170)the Natural Science Foundation of Shanghai Municipal(No.13ZR1422500)
文摘Let F_q be a finite field of characteristic p. In this paper, by using the index sum method the authors obtain a sufficient condition for the existence of a primitive elementα∈ F_(q^n) such that α + α^(-1)is also primitive or α + α^(-1)is primitive and α is a normal element of F_(q^n) over F_q.
