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.
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.
@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}, pages = {1--11}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {32}, number = {4}, year = {1982}, doi = {10.5802/aif.891}, zbl = {0489.10038}, mrnumber = {84m:10033}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.891/} }
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 SP - 1 EP - 11 VL - 32 IS - 4 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.891/ DO - 10.5802/aif.891 LA - en ID - AIF_1982__32_4_1_0 ER -
%0 Journal Article %A Deshouillers, Jean-Marc %A Iwaniec, Henryk %T On the greatest prime factor of $n^2+1$ %J Annales de l'Institut Fourier %D 1982 %P 1-11 %V 32 %N 4 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.891/ %R 10.5802/aif.891 %G en %F 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, Volume 32 (1982) no. 4, pp. 1-11. doi : 10.5802/aif.891. https://aif.centre-mersenne.org/articles/10.5802/aif.891/
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