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}, pages = {1--11}, publisher = {Institut Fourier}, volume = {32}, number = {4}, year = {1982}, doi = {10.5802/aif.891}, zbl = {0489.10038}, mrnumber = {84m:10033}, language = {en}, url = {www.numdam.org/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) no. 4, pp. 1-11. doi : 10.5802/aif.891. http://www.numdam.org/item/AIF_1982__32_4_1_0/
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