Largest Prime Factors of Polynomials
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866912427564597248 |
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| author | Carella, N. A. |
| author_facet | Carella, N. A. |
| contents | 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 $p \geq x^{1.279}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_10075 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Largest Prime Factors of Polynomials Carella, N. A. General Mathematics Primary 11N05, Secondary 11N32 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 $p \geq x^{1.279}$. |
| title | Largest Prime Factors of Polynomials |
| topic | General Mathematics Primary 11N05, Secondary 11N32 |
| url | https://arxiv.org/abs/2308.10075 |