On the greatest prime factor of $n^2+1$

Deshouillers, Jean-Marc, and Iwaniec, Henryk. "On the greatest prime factor of $n^2+1$." Annales de l'institut Fourier 32.4 (1982): 1-11. <http://eudml.org/doc/74560>.

@article{Deshouillers1982,
abstract = {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.},
author = {Deshouillers, Jean-Marc, Iwaniec, Henryk},
journal = {Annales de l'institut Fourier},
keywords = {greatest prime factor; combination of Hooley's method; upper bound for Kloosterman sums},
language = {eng},
number = {4},
pages = {1-11},
publisher = {Association des Annales de l'Institut Fourier},
title = {On the greatest prime factor of $n^2+1$},
url = {http://eudml.org/doc/74560},
volume = {32},
year = {1982},
}

TY - JOUR
AU - Deshouillers, Jean-Marc
AU - Iwaniec, Henryk
TI - On the greatest prime factor of $n^2+1$
JO - Annales de l'institut Fourier
PY - 1982
PB - Association des Annales de l'Institut Fourier
VL - 32
IS - 4
SP - 1
EP - 11
AB - 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.
LA - eng
KW - greatest prime factor; combination of Hooley's method; upper bound for Kloosterman sums
UR - http://eudml.org/doc/74560
ER -