On the greatest prime factor of \((n^2)+1\)
type: Item
instance of: scholarly article
title: On the greatest prime factor of \((n^2)+1\)
zbMATH Open document ID: 0489.10038
author: Jean-Marc Deshouillers
author: H. Iwaniec
publication date: 1982-01-01T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/74560
review text: There exist infinitely many integers \(n\) such that the greatest prime factor of \(n^2 + 1\) is at least \(n^{6/5}\). The proof is a combination of Hooley's method -- for reducing the problem to the evaluation of Kloosterman sums -- and the majorization of Kloosterman sums on average due to the authors.
Mathematics Subject Classification ID: 11N05
Mathematics Subject Classification ID: 11L05
zbMATH DE Number: 3769748
zbMATH Keywords: greatest prime factor
zbMATH Keywords: combination of Hooley's method
zbMATH Keywords: upper bound for Kloosterman sums
MaRDI profile type: Publication
OpenAlex ID: W2018314941
cites work: Kloosterman sums and Fourier coefficients of cusp forms
cites work: On the greatest prime factor of a quadratic polynomial
cites work: Q4092051
cites work: Rosser's sieve
DOI: 10.5802/AIF.891
published in: Annales de l’institut Fourier
description: scientific article; zbMATH DE number 3769748