收稿日期: 2014-12-12
修回日期: 2015-04-23
网络出版日期: 2015-09-15
基金资助
Supported by the National Natural Science Foundation of China (11271363)
The number of solutions of some equations over finite fields
Received date: 2014-12-12
Revised date: 2015-04-23
Online published: 2015-09-15
Supported by
Supported by the National Natural Science Foundation of China (11271363)
宋佳 , 陈玉福 . 有限域上某些方程的解数公式[J]. 中国科学院大学学报, 2015 , 32(5) : 582 -587 . DOI: 10.7523/j.issn.2095-6134.2015.05.002
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=cx1…xt
and
(x1+…+xn)2=cx1…xt
under some certain restrictions, where mj|q-1,n≥2,c∈Fq*,t > n. When m1=…=mn=m, an explicit formula for the number of solutions of the equation x1m+…+xnm=cx1…xt is presented.
Key words： finite field; solutions of equation; diagonal equation
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