On the largest prime factor of quadratic polynomials

Runbo Li

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arXiv · 2406.07575

On the largest prime factor of quadratic polynomials

Runbo Li

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Abstract

Let $x$ denote a sufficiently large integer. We show that the recent result of Grimmelt and Merikoski actually yields the largest prime factor of $n^2 +1$ is greater than $x^{1.317}$ infinitely often. As an application, we give a new upper bound for the number of integers $n \leqslant x$ which $n^2 +1$ has a primitive divisor.

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Runbo Li. 2024-06-06. On the largest prime factor of quadratic polynomials. https://arxiv.org/abs/2406.07575

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