|本期目录/Table of Contents|

一个包含欧拉函数的方程(PDF)

《纯粹数学与应用数学》[ISSN:1008-5513/CN:61-1240/O1]

期数:
2010年01期
页码:
96
栏目:
出版日期:
2010-01-15

文章信息/Info

Title:
An equation involving Euler-totient function
作者:
田呈亮1 付静2 白维祖3
(1.山东大学数学学院, 山东济南250100; 2.长春师范学院数学系, 吉林长春130032; 3.甘肃省电力设计院, 甘肃兰州730050)
Author(s):
TIAN Cheng-liang1 FU Jing2 BAI Wei-zu3
(1.School of Mathematics, Shandong University, Ji'nan 250100, China; 2.Department of Mathematics, Changchun Normal University, Changchun 130032, China; 3.Gansu Electric Power Design Institute, Lanzhou 730050, China)
关键词:
Euler函数 方程 正整数解
Keywords:
Euler totient function equation positive integer solutions
分类号:
O156.4
DOI:
-
文献标识码:
A
摘要:
设n为任意正整数, 如果n > 1, 设n = p?1 1 p?2 2 ¢ ¢ ¢ p?k k 是n的标准分解式, 函 数-(n)定义为-(1) = 0; -(n) = Pk i=1 ?i, á(n)为Euler函数, 本文的主要目的是利用初 等方法研究方程á(á(n)) = 2-(n)的可解性, 并获得该方程的所有正整数解, 从而彻底解 决了前学者提出的一个问题.
Abstract:
For any positive integer n, we deˉne the arithmetical function -(n) as -(1) = 0; If n > 1 and n = p?1 1 p?2 2 ¢ ¢ ¢ p?k k be the prime powers factorization of n, then -(n) = Pk i=1 ?i. á(n) denotes the Euler- totient function. The main purpose of this paper is using the elementary to study the solutions of the equation á(á(n)) = 2-(n), and give all positive integer solutions. Namely, the problem proposed by before scholar is solved completely.

参考文献/References

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备注/Memo

备注/Memo:
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更新日期/Last Update: 2010-01-15