On the representation of rational numbers via Euler's totient function
Fuente:
arXiv
Salvato in:
| Autori principali: | , , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866913706711973888 |
|---|---|
| author | Zhang, Weilin Chen, Fengyuan Li, Hongjian Yuan, Pingzhi |
| author_facet | Zhang, Weilin Chen, Fengyuan Li, Hongjian Yuan, Pingzhi |
| contents | Let $b>1$ be an odd positive integer and $k, l \in \mathbb{N}$. In this paper, we show that every positive rational number can be written as $φ(m^{2})/(φ(n^{2}))^{b}$ and $φ(k(m^{2}-1))/φ(ln^{2})$, where $m, n\in \mathbb{N}$ and $φ$ is the Euler's totient function. At the end, some further results are discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18252 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the representation of rational numbers via Euler's totient function Zhang, Weilin Chen, Fengyuan Li, Hongjian Yuan, Pingzhi Number Theory Let $b>1$ be an odd positive integer and $k, l \in \mathbb{N}$. In this paper, we show that every positive rational number can be written as $φ(m^{2})/(φ(n^{2}))^{b}$ and $φ(k(m^{2}-1))/φ(ln^{2})$, where $m, n\in \mathbb{N}$ and $φ$ is the Euler's totient function. At the end, some further results are discussed. |
| title | On the representation of rational numbers via Euler's totient function |
| topic | Number Theory |
| url | https://arxiv.org/abs/2502.18252 |