关于Euler函数方程和Smarandache函数相关问题的研究

发布时间：2018-05-18 02:24

本文选题：Euler函数 + Smarandache双阶乘函数　；参考：《延安大学》2017年硕士论文

【摘要】：摘要:在数论中,不定方程的解和函数的均值问题占有非常重要的地位.国内外众多数学学者对此进行了深入的研究,并取得许多卓越的成绩.基于此,本文采用初等数论和解析数论中的相关理论和方法,对Euler函数和Smarandache函数的性质做了进一步的研究.具体来说,文章的主要内容包括以下几个方面:1.运用初等方法讨论了 Euler函数方程φ(xy)=m(φ(x)+φ(y))当m= 6,3k以及φ(xyz)=m(φ(x)+ φ(y)+φ(z))当m=10时的可解性问题,并得出他们的所有正整数解.2.运用分类讨论的方法研究了包含Euler函数φ(n)和Smarandache双阶乘函数Sdf(n)的方程Sdf(n)= 2φ(n)的可解性问题,并给出方程的所有正整数解.3.利用解析方法研究了 Smarandache双阶乘函数Sdf(n)与素因子个数函数Ω(n)的混合均值,并得到如下渐近公式(?)其中ai(i=1,2,…,k)为可计算常数.
[Abstract]:Absrtact: in number theory, the solution of indefinite equation and the mean value of function play an important role. Many mathematics scholars at home and abroad have carried on the thorough research, and obtained many outstanding achievements. Based on this, the properties of Euler function and Smarandache function are further studied by using the relevant theories and methods of elementary number theory and analytic number theory. Specifically, the main content of the article includes the following aspects: 1. In this paper, we discuss the solvability problem of the Euler function equation 蠁 (蠁 X) 蠁 y) when m = 6 ~ 3k and 蠁 ~ (?) m = 10:00 by using elementary method, and obtain all their positive integer solutions .2.The problem of the solvability of the Euler function equation is discussed by means of elementary method, and all the positive integer solutions of the equation m = 6 ~ 3k are obtained. By using the method of classification discussion, the solvability of equations containing Euler function 蠁 n) and Smarandache double factorial function Sdfn n = 2 蠁 n is studied, and all positive integer solutions. 3 of the equation are given. The mixed mean value of Smarandache double factorial function Sdfn) and prime factor number function 惟 n) is studied by analytic method, and the following asymptotic formulas are obtained. Among them, 1, 1, 2,. K) is a computable constant.
【学位授予单位】：延安大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O156

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