On the use of explicit bounds on residues of Dedekind zeta functions taking into account the behavior of small primes

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.

Further developments in the comparative prime-number theory III

P. Turán, Stanisław Knapowski (1965)

Acta Arithmetica

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On primes in arithmetic progressions

J. van Lint, H. Richert (1965)

Acta Arithmetica

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