| 有限域上某些方程的解数公式 |
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| 作者姓名： | 宋佳 陈玉福 |
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| 作者单位： | 中国科学院大学数学科学学院, 北京 101408 |
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| 基金项目： | Supported by the National Natural Science Foundation of China (11271363) |
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| 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=cx1…xt
和
(x1+…+xn)2=cx1…xt
在一定条件下的解数公式, 其中mj|q-1,n≥2,c∈Fq*,t > n.当m1=…=mn=m时, 给出了方程x1m+…+xnm=cx1…xt的解数的显示公式.
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| 关 键 词： | 有限域 方程的解数 对角方程 |
| 收稿时间： | 2014-12-12 |
| 修稿时间： | 2015-04-23 |
The number of solutions of some equations over finite fields |
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| Authors: | SONG Jia CHEN Yufu |
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| Institution: | School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 101408, China |
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| 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=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. |
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| Keywords: | finite field solutions of equation diagonal equation |
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