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机构地区:[1]四川师范大学数学与软件科学学院,四川成都610066
出 处:《四川师范大学学报(自然科学版)》2015年第6期797-801,共5页Journal of Sichuan Normal University(Natural Science)
基 金:国家自然科学基金(11401408);四川省教育厅重点项目(14ZA0034)
摘 要: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.Let F_q be the q elements finite field. The literature( P. P. Wang, et al. Finite Fields and Their Applications,2012,18 (4) : 800 - 813. ) obtains several sufficient conditions for the existence of a F_q such that a and a + α+α^-1 are both primitive elements in F_q. Recently, the work( Q. Y. Liao, et al. Chin Annals Math,2015, in press. ) generalizes their main results to the finite field with arbitrary characteristics. In this paper, we obtain a sufficient condition for the existence of the finite field F_q in which there exist two primitive elements α,β E =F_q, such that α+β is also a primitive element of.F_q. Furthermore, for finite fields satisfying this condi- tion, by using character sums, we get a lower bound of the corresponding q. Finally, we verify that the condition is true for all finite fields with characteristic 2 except F_2 and F_4
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