How smooth is \(\varphi(2^n+3)\)?
type: Item
instance of: scholarly article
title: How smooth is \(\varphi(2^n+3)\)?
zbMATH Open document ID: 1063.11031
author: Florian Luca
published in: Rocky Mountain Journal of Mathematics
publication date: 2005-03-10T00:00:00Z
review text: If \(n\) is any integer, denote the largest prime divisor of \(n\) by \(P(n)\). The author proves that \(P(\varphi(2^n+3))\) tends to infinity with \(n\) on a set of \(n\) with asymptotic density \(1\), where \(\varphi(*)\) is Euler's totient. He also establishes a certain lower bound with respect to \(P(\varphi(| u_n|))\) where \((u_n)_{n\geq0}\) is a binary recurrent sequence of integers, but too technical to state here.
reviewed by: Richard A. Mollin
Mathematics Subject Classification ID: 11N25
Mathematics Subject Classification ID: 11J61
zbMATH DE Number: 2143233
zbMATH Keywords: Euler phi-function
zbMATH Keywords: Fermat number
zbMATH Keywords: prime
zbMATH Keywords: recurrent sequence
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181069806
OpenAlex ID: W2060568071
DOI: 10.1216/RMJM/1181069806
description: scientific article; zbMATH DE number 2143233