论文标题
跨越方法和莱默的基本问题
The spanning method and the Lehmer totient problem
论文作者
论文摘要
在本文中，我们介绍并开发了整数沿函数的跨度概念$ f：\ mathbb {n} \ longrightarrow \ mathbb {r} $。我们将此方法应用于需要确定$ tf（n）= n-k $的方程是否具有解决方案的$ n \ in \ mathbb {n} $中的解决方案$ n \ in \ mathbb {n} $和一些$ t \ in \ mathbb {n} $。特别是，我们表明\ begin {align} \＃\ {n \ leq s〜 | 〜tφ（n）+1 = n，〜\ mathbf {for〜mathbf {for〜some} 〜t \ in \ in \ Mathbb {n} \} \} \} \} \ geq Q Q Q Q Q \ geq \ frac {s} \lfloor s\rfloor }(1-\frac{1}{p})^{-1}-\frac{3}{2}e^γ\nonumber \end{align}for $s\geq s_o$, where $φ$ is the Euler totient function and $γ=0.5772\cdots$ is the Euler-Macheroni常数。
In this paper we introduce and develop the notion of spanning of integers along functions $f:\mathbb{N}\longrightarrow \mathbb{R}$. We apply this method to a class of problems requiring to determine if the equations of the form $tf(n)=n-k$ has a solution $n\in \mathbb{N}$ for a fixed $k\in \mathbb{N}$ and some $t\in \mathbb{N}$. In particular, we show that \begin{align} \# \{n\leq s~|~tφ(n)+1=n,~\mathbf{for~some}~t\in \mathbb{N}\}\geq \frac{s}{2\log s}\prod \limits_{p | \lfloor s\rfloor }(1-\frac{1}{p})^{-1}-\frac{3}{2}e^γ\nonumber \end{align}for $s\geq s_o$, where $φ$ is the Euler totient function and $γ=0.5772\cdots$ is the Euler-Macheroni constant.
