首页 | 本学科首页   官方微博 | 高级检索  
     

二次剩余问题的一个新定理
引用本文:张韶华. 二次剩余问题的一个新定理[J]. 数学杂志, 2007, 27(1): 15-18
作者姓名:张韶华
作者单位:山东大学数学与系统科学学院,山东济南,250100;武汉船舶通信研究所,湖北武汉,430079
基金项目:Acknow ledgement. I thank Prof. Chen Gongliang, Dr Zhou Guangming and Prof. Yan Xinrong for their helpful comments.
摘    要:
研究了二次剩余问题,利用整数分类的办法,给出了|Jn|和|Qn|的公式(这里n是奇合数,Jn是Zn*中有Jacobi符号为1的所有元素的集合,Qn是模n的所有二次剩余的集合) .基于这些结果,可以得出当a对模n的Jacobi符号等于1时,正确猜测a为模n的二次剩余的可能性,从而推广了[1]p .74中的结果.

关 键 词:二次剩余问题  Jacobi符号  Legendre符号  二次剩余
文章编号:0255-7797(2007)01-0015-04
修稿时间:2005-06-102005-12-19

A NEW THEOREM ABOUT THE QUADRATIC RESIDUOSITY PROBLEM
ZHANG Shao-hua. A NEW THEOREM ABOUT THE QUADRATIC RESIDUOSITY PROBLEM[J]. Journal of Mathematics, 2007, 27(1): 15-18
Authors:ZHANG Shao-hua
Affiliation:1. School of Math. and System Science, Shandong University, Jinan 250100, China;2. Wuhan Maritime Communications Research Institute, Wuhan 430079, China
Abstract:
In this paper, we study the quadratic residuosity problem (QRP). Using the methods of integer classification, we give formulae of |J_ n | and |Q_ n | for a given odd composite interger n, where J_ n is the set of all elements in Z _ n having Jacobi symbol 1 and Q_ n is the set of all quadratic residues modulo n. Based on these results, one can obtain the probability of a correct guess that a is a quadratic residue modulo n and generalize the result in [1] p.74, where a is a positive integer modulo n having Jacobi symbol 1.
Keywords:the quadratic residuosity problem  Jacobi symbol  Legendre symbol  quadratic residue
本文献已被 CNKI 维普 万方数据 等数据库收录!
设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号