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中国科学院大学学报 ›› 2015, Vol. 32 ›› Issue (5): 582-587.DOI: 10.7523/j.issn.2095-6134.2015.05.002

• 数学与物理学 • 上一篇    下一篇

有限域上某些方程的解数公式

宋佳, 陈玉福   

  1. 中国科学院大学数学科学学院, 北京 101408
  • 收稿日期:2014-12-12 修回日期:2015-04-23 发布日期:2015-09-15
  • 通讯作者: 宋佳
  • 基金资助:

    Supported by the National Natural Science Foundation of China (11271363)

The number of solutions of some equations over finite fields

SONG Jia, CHEN Yufu   

  1. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China
  • Received:2014-12-12 Revised:2015-04-23 Published:2015-09-15
  • Supported by:

    Supported by the National Natural Science Foundation of China (11271363)

摘要:

给出有限域Fq(q=ps, s≥1, p是一个奇素数)上的方程
x1m1+…+xnmn=cx1xt

(x1+…+xn)2=cx1xt
在一定条件下的解数公式, 其中mj|q-1,n≥2,cFq*,t > n.当m1=…=mn=m时, 给出了方程x1m+…+xnm=cx1xt的解数的显示公式.

关键词: 有限域, 方程的解数, 对角方程

Abstract:

Let Fq be a finite field with q=ps (s≥1) elements, where p is an odd prime number. In this paper, we present formulas for the number of solutions of the following equations defined over Fq
x1m1+…+xnmn=cx1xt
and
(x1+…+xn)2=cx1xt
under some certain restrictions, where mj|q-1,n≥2,cFq*,t > n. When m1=…=mn=m, an explicit formula for the number of solutions of the equation x1m+…+xnm=cx1xt is presented.

Key words: finite field, solutions of equation, diagonal equation

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