一类同余方程解数的上界估计

上海大学学报(自然科学版) ›› 2010, Vol. 16 ›› Issue (2): 163-169.

一类同余方程解数的上界估计

冯上海

上海大学理学院，上海 200444

收稿日期:2008-12-12 出版日期:2010-04-20 发布日期:2010-04-20
通讯作者: 冯上海(1985~)，男，硕士研究生,研究方向为解析数论. E-mail:fengshh2301@163.com

Estimation of Upper Bound for the Number of Solutions of a Kind of Congruence

FENG Shang-Hai

College of Sciences, Shanghai University, Shanghai 200444, China

Received:2008-12-12 Online:2010-04-20 Published:2010-04-20

摘要/Abstract

摘要：

主要研究同余方程∏ri=1(x+m_i)≡∏2r i=r+1(x+m_i)(mod p^μ)有解时, 关于m=(m₁,m₂,…,m_2r)解数的问题.通过引入p-adic指数赋值,并比较该同余方程关于未知元x各项系数的p-adic指数赋值方法,得到r=6时,该同余方程关于m解数的上界估计.

关键词: 同余方程;解数;p-adic指数赋值;特征和

Abstract:

The problem of the solution number about m=(m₁,m₂,…,m_2r) was studied, when the congruence can be solved. By introducing the conception of the p-adic exponential evaluation and comparing the p-adic exponential evaluations of each coefficient of x in the congruence, we obtain the solution number of m in the congruence when r=6.

Key words: congruence; number of solutions; p-adic exponential evaluation; character sum

中图分类号:

O 156.4

冯上海. 一类同余方程解数的上界估计[J]. 上海大学学报(自然科学版), 2010, 16(2): 163-169.

FENG Shang-Hai. Estimation of Upper Bound for the Number of Solutions of a Kind of Congruence[J]. Journal of Shanghai University（Natural Science Edition）, 2010, 16(2): 163-169.