Publications and Research
Document Type
Article
Publication Date
Summer 8-5-2023
Abstract
A pair of integers $n$ and $n+k$ is a simultaneous solution of an arithmetic function $f:\mathbb{N}\longrightarrow \mathbb{R}$ if $f(n)=f(n+k)$, where $k\ne0$ is a fixed integer. This article shows that the totient function has infinitely many simultaneous solutions. In particular, $\varphi(n)=\varphi(n+2)$ infinitely often as $n\to\infty$.
