Simultaneous Values of the Totient Function

Authors

Nelson Carella, CUNY Bronx Community CollegeFollow

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 $n\to\infty$.

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