[1]王 容,廖群英*.关于广义欧拉函数φ5(n)[J].四川师范大学学报(自然科学版),2018,(04):445-449.[doi:10.3969/j.issn.1001-8395.2018.04.003]
 WANG Rong,LIAO Qunying.On the Generalized Euler Function φ5(n)[J].Journal of SichuanNormal University,2018,(04):445-449.[doi:10.3969/j.issn.1001-8395.2018.04.003]
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《四川师范大学学报(自然科学版)》[ISSN:1001-8395/CN:51-1295/N]

卷:
期数:
2018年04期
页码:
445-449
栏目:
基础理论
出版日期:
2018-04-15

文章信息/Info

Title:
On the Generalized Euler Function φ5(n)
文章编号:
1001-8395(2018)04-0445-05
作者:
王 容 廖群英*
四川师范大学 数学与软件科学学院, 四川 成都 610066
Author(s):
WANG Rong LIAO Qunying
College of Mathematics and Software Science, Sichuan Normal University, Chengdu 610066, Sichuan
关键词:
欧拉函数 广义欧拉函数 麦比乌斯函数
Keywords:
Euler function generalized Euler functionbius function
分类号:
O156.1
DOI:
10.3969/j.issn.1001-8395.2018.04.003
文献标志码:
A
摘要:
为将Lehmer同余式从模素数的平方推广到模任意整数的平方,前人定义了正整数n的广义欧拉函数φe(n),其中e为正整数,并完全确定了φe(n)(e=3,4,6)的准确计算公式.进一步研究利用初等的方法和技巧给出部分正整数n的φ5(n)的准确计算公式,由此得到相应的φ5(n)的奇偶性判别.
Abstract:
In 2007, for the well-known Lehmer congruence formula, to generalize the modulo from the square of prime numbers to the square of an arbitrary integer, previous researchers defined the generalized Euler function φe(n)(e∈Z+)for a positive integer n, and determined the explicit formula for φe(n)(e=3,4,6).This paper further studies the accurate calculation formula of the generalized Euler function.On the basis of the elementary methods and techniques, the calculation formula of φ5(n) for several classes of positive integers is obtained, and then the parity of the corresponding φ5(n) is given.

参考文献/References:

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[7] 蔡天新,沈忠燕,胡孟君.广义欧拉函数的奇偶性(英)[J].数学进展,2013,42(4):505-510.
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备注/Memo

备注/Memo:
收稿日期:2016-11-28 接受日期:2017-04-14
基金项目:国家自然科学基金(11401408)和四川省科技厅重点项目(2016JY0134)
*通信作者简介:廖群英(1974—),女,教授,主要从事编码与密码学理论的研究,E-mail:qunyingliao@sicnu.edu.cn
更新日期/Last Update: 2018-04-15