Relations in the Set of Divisors of an Integer $n$
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866910647514562560 |
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| author | Letendre, Patrick |
| author_facet | Letendre, Patrick |
| contents | Let $\mathcal{D}_{n} \subset \mathbb{N}$ be the set of the $τ(n)$ divisors of $n$. We generalize a method developed by Erd\H os, Tenenbaum and de la Bretèche for the study of the set $\mathcal{D}_{n}$. In particular, using these ideas, we establish that $$ |\{(d_{1},d_{2},d_{3}) \in \mathcal{D}_{n}^3 : d_{1}+d_{2}=d_{3}\}| \le τ(n)^{2-δ} $$ with $δ=0.045072$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_17424 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relations in the Set of Divisors of an Integer $n$ Letendre, Patrick Number Theory 11N37, 11N56, 11N64 Let $\mathcal{D}_{n} \subset \mathbb{N}$ be the set of the $τ(n)$ divisors of $n$. We generalize a method developed by Erd\H os, Tenenbaum and de la Bretèche for the study of the set $\mathcal{D}_{n}$. In particular, using these ideas, we establish that $$ |\{(d_{1},d_{2},d_{3}) \in \mathcal{D}_{n}^3 : d_{1}+d_{2}=d_{3}\}| \le τ(n)^{2-δ} $$ with $δ=0.045072$. |
| title | Relations in the Set of Divisors of an Integer $n$ |
| topic | Number Theory 11N37, 11N56, 11N64 |
| url | https://arxiv.org/abs/2404.17424 |