On the periodicity of some Farhi arithmetical functions
| dc.creator | Ji, Qing-Zhong | |
| dc.creator | Ji, Chun-Gang | |
| dc.date | 2009-03-06 | |
| dc.date | 2009-05-03 | |
| dc.date.accessioned | 2026-07-07T13:10:48Z | |
| dc.date.available | 2026-07-07T13:10:48Z | |
| dc.description | Let $k\in\mathbb{N}$. Let $f(x)\in \Bbb{Z}[x]$ be any polynomial such that $f(x)$ and $f(x+1)f(x+2)... f(x+k)$ are coprime in $\mathbb{Q}[x]$. We call $$g_{k,f}(n):=\frac{|f(n)f(n+1)... f(n+k)|}{\text{lcm}(f(n),f(n+1),...,f(n+k))}$$ a Farhi arithmetic function. In this paper, we prove that $g_{k,f}$ is periodic. This generalizes the previous results of Farhi and Kane, and Hong and Yang. | |
| dc.description | 14 page | |
| dc.identifier | https://arxiv.org/abs/0903.1162 | |
| dc.identifier | http://arxiv.org/abs/0903.1162 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/229100 | |
| dc.subject | Number Theory | |
| dc.subject | Commutative Algebra | |
| dc.subject | 11A05 | |
| dc.title | On the periodicity of some Farhi arithmetical functions | |
| dc.type | text |