On the largest value of the solutions of Erdős's last equation
Fuente:
arXiv
Enregistré dans:
| Auteurs principaux: | , |
|---|---|
| Format: | Preprint |
| Publié: |
2024
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866912109186514944 |
|---|---|
| author | Pink, István Sándor, Csaba |
| author_facet | Pink, István Sándor, Csaba |
| contents | Let $n$ be a positive integer. The Diophantine equation $n(x_1+x_2+\dots +x_n)=x_1x_2\dots x_n$, $1 \le x_1\le x_2\le \dots \le x_n$ is called Erdős's last equation. We prove that $x_n\to \infty $ as $n\to \infty$ and determine all tuples $(n,x_1,\dots ,x_n)$ with $x_n\le 10$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_04764 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the largest value of the solutions of Erdős's last equation Pink, István Sándor, Csaba Number Theory 11D45, 11D72 Let $n$ be a positive integer. The Diophantine equation $n(x_1+x_2+\dots +x_n)=x_1x_2\dots x_n$, $1 \le x_1\le x_2\le \dots \le x_n$ is called Erdős's last equation. We prove that $x_n\to \infty $ as $n\to \infty$ and determine all tuples $(n,x_1,\dots ,x_n)$ with $x_n\le 10$. |
| title | On the largest value of the solutions of Erdős's last equation |
| topic | Number Theory 11D45, 11D72 |
| url | https://arxiv.org/abs/2411.04764 |