有限域上一类方程解数的注记  

Remarks on the number of solutions tocertain equations over finite fields

作　　者：徐碧云 姜坤 曹炜 Xu Biyun;Jiang Kun;Cao Wei(School of Mathematics and Statistics,Ningbo University,Ningbo 315211,China)

机构地区：[1]宁波大学数学与统计学院,浙江宁波315211

出　　处：《纯粹数学与应用数学》2021年第2期188-197,共10页Pure and Applied Mathematics

基　　金：国家自然科学基金(11871291);宁波市自然科学基金(2019A610035).

摘　　要：设Fq是含有q个元素的有限域,其中q=p^(r),r≥1,p是奇素数.研究了有限域Fq上Markoff-Hurwitz类型方程,并给出了当其增广次数矩阵在剩余类环Z/(q−1)Z中可逆时其解数公式的组合证明方法.进一步研究了其推广形式,并得到了此推广形式的方程在特殊条件下的解数公式.Let Fq be a finite field of q elements,where q=p^( r),r≥1,and p is an odd prime number.We study the Markoff-Hurwitz-type equation in Fq,and provide a combinatorial proof to the formula for the number of solutions to it when the augmented degree matrix is invertible in the residue class ring Z/(q−1)Z.We also consider its generalization,and obtain the formula for the number of solutions to it in Fq under special conditions.

关 键 词：有限域 Markoff-Hurwitz类型方程 增广次数矩阵 高斯和 

分 类 号：O156.2[理学—数学]