Il existe une infinité d’entiers tels que le plus grand facteur premier de soit au moins . La démonstration de ce résultat combine la méthode de Hooley – pour ramener le problème à l’évaluation de sommes de Kloosterman – et la majoration de sommes de Kloosterman en moyenne obtenue par les auteurs.
There exist infinitely many integers such that the greatest prime factor of is at least . 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.
@article{AIF_1982__32_4_1_0,
author = {Deshouillers, Jean-Marc and Iwaniec, Henryk},
title = {On the greatest prime factor of $n^2+1$},
journal = {Annales de l'Institut Fourier},
volume = {32},
year = {1982},
pages = {1-11},
doi = {10.5802/aif.891},
mrnumber = {84m:10033},
zbl = {0489.10038},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_1982__32_4_1_0}
}
Deshouillers, Jean-Marc; Iwaniec, Henryk. On the greatest prime factor of $n^2+1$. Annales de l'Institut Fourier, Tome 32 (1982) pp. 1-11. doi : 10.5802/aif.891. http://gdmltest.u-ga.fr/item/AIF_1982__32_4_1_0/
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