On the greatest prime factor of \((n^2)+1\)
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.
scientific article; zbMATH DE number 3769748