Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2405.11600 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917830008504320 |
|---|---|
| author | Sándor, Csaba Zakarczemny, Maciej |
| author_facet | Sándor, Csaba Zakarczemny, Maciej |
| contents | Denote by $N(n)$ the number of integer solutions $(x_1,\,x_2,\ldots ,x_n)$ of the equation $x_1+x_2+\ldots+x_n=x_1x_2\cdot\ldots\cdot x_n$ such that $x_1\ge x_2\ge\ldots\ge x_n\ge 1$, $n \in \mathbb{Z}^+$. The aim of this paper are is twofold: first we present an asymptotic formula for $\sum\limits_{2\le n\le x}N(n)$, then we verify that the counting function $N(n)$ takes very large value compared to its average value. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_11600 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Equal Sum and Product Problem III Sándor, Csaba Zakarczemny, Maciej Number Theory Denote by $N(n)$ the number of integer solutions $(x_1,\,x_2,\ldots ,x_n)$ of the equation $x_1+x_2+\ldots+x_n=x_1x_2\cdot\ldots\cdot x_n$ such that $x_1\ge x_2\ge\ldots\ge x_n\ge 1$, $n \in \mathbb{Z}^+$. The aim of this paper are is twofold: first we present an asymptotic formula for $\sum\limits_{2\le n\le x}N(n)$, then we verify that the counting function $N(n)$ takes very large value compared to its average value. |
| title | Equal Sum and Product Problem III |
| topic | Number Theory |
| url | https://arxiv.org/abs/2405.11600 |