On the greatest prime factor of \((n^2)+1\) (Q1166560)
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scientific article; zbMATH DE number 3769748
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the greatest prime factor of \((n^2)+1\) |
scientific article; zbMATH DE number 3769748 |
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On the greatest prime factor of \((n^2)+1\) (English)
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1982
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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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greatest prime factor
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combination of Hooley's method
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upper bound for Kloosterman sums
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