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›› 2015, Vol. 32 ›› Issue (5): 582-587.DOI: 10.7523/j.issn.2095-6134.2015.05.002

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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 Online:2015-09-15
  • Supported by:

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

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

CLC Number: