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arXiv · 2308.10075

Largest Prime Factors of Polynomials

N. A. Carella
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Abstract

Let $x>1$ be a large number. This note shows that the largest prime factor of the quadratic product $\prod_{x\leq n\leq 2x}\left(n^2+1 \right)$ satisfies the relation $p \geq x^{3/2}$ as $x$ tends to infinity. This improves the current estimate $p \geq x^{1.279}$.

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N. A. Carella. 2023-08-19. Largest Prime Factors of Polynomials. https://arxiv.org/abs/2308.10075

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