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On the greatest prime factor of n 2 + 1

Jean-Marc Deshouillers, Henryk Iwaniec (1982)

Annales de l'institut Fourier

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.

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