[1]肖 瑞,杨 昊,周云秀,等.多个正整数的最大公因数与最小公倍数的几个计算关系[J].成都信息工程大学学报,2020,35(02):244-245.[doi:10.16836/j.cnki.jcuit.2020.02.017]
XIAO Rui,YANG Hao,ZHOU Yunxiu,et al.Several Calculation Relationships between the Greatest Common Divisor and the Least Common Multiple[J].Journal of Chengdu University of Information Technology,2020,35(02):244-245.[doi:10.16836/j.cnki.jcuit.2020.02.017]
点击复制
XIAO Rui,YANG Hao,ZHOU Yunxiu,et al.Several Calculation Relationships between the Greatest Common Divisor and the Least Common Multiple[J].Journal of Chengdu University of Information Technology,2020,35(02):244-245.[doi:10.16836/j.cnki.jcuit.2020.02.017]
多个正整数的最大公因数与最小公倍数的几个计算关系
成都信息工程大学学报[ISSN:1006-6977/CN:61-1281/TN]
卷:
35
期数:
2020年02期
页码:
244-245
栏目:
数理科学
出版日期:
2020-04-30
- Title:
- Several Calculation Relationships between the Greatest Common Divisor and the Least Common Multiple
- 文章编号:
- 2096-1618(2020)02-0244-04
- Keywords:
- greatest common divisor; least common multiple; pure mathematics; coding and cryptography theory
- 分类号:
- O156.1
- 文献标志码:
- A
- 摘要:
- 熟知对任意正整数a,b,c,有[a,b]=(ab)/((a,b)),[(a,c),(b,c)]=([a,b],c),其中[ ],( )分别表示最小公倍数和最大公因数.在RSA公钥算法中涉及两个正整数的最小公倍数和最大公因数的相关计算.为了给传统的RSA算法提供可能的优化方案,利用初等的方法与技巧,对任意多个正整数的最大公因数和最小公倍数的计算关系做了相关探究,推广了上述结果,给出了任意多个正整数的最大公因数和最小公倍数之间的3种计算关系.
- Abstract:
- It's well-known that for any positive integers a,b,c,[a,b]=(ab)/((a,b)),[(a,c),(b,c)]=([a,b],c),where [ ] and( )represent the least common divisor and the greatest multiply, respectively. The RSA algorithm involved the related calculation of the greatest common divisor and the least common multiple. In order to provide a possible optimization scheme for the traditional RSA algorithm, the present paper takes advantage of the elementary methods and skills to explore the calculation relationship between the greatest common divisor and the least common multiple of any positive integers. The result mentioned above is promoted to obtain three calculation relationships between the greatest common divisor and the least common multiple of any positive integers.
参考文献/References:
[1] 陈全国,刘淼.关于最大公因数和最小公倍数的一点注记[J].牡丹江大学学报,2014,23(10):141-142.
[2] 刘娅茹.安全多方计算中两个基础问题的研究[D].西安:西安科技大学,2018.
[3] 朱文余,孙琦.计算机密码应用基础[M].北京:科学出版社,2000.
[4] 闵嗣鹤,严士健.初等数论[M].3版.北京:高等教育出版社,2003.
[5] 汤剑红.求多个数的最大公约数的算法设计[J].计算机时代,2012(6):21-22.
备注/Memo
收稿日期:2019-11-03 基金项目:四川省科技厅科研重点资助项目(2016JY0134)
更新日期/Last Update:
2020-04-30