Regular integers modulo n
| dc.creator | Tóth, László | |
| dc.date | 2007-10-10 | |
| dc.date | 2008-09-01 | |
| dc.date.accessioned | 2026-07-07T09:59:19Z | |
| dc.date.available | 2026-07-07T09:59:19Z | |
| dc.description | Let $n=p_1^{ν_1}... p_r^{ν_r} >1$ be an integer. An integer $a$ is called regular (mod $n$) if there is an integer $x$ such that $a^2x\equiv a$ (mod $n$). Let $\varrho(n)$ denote the number of regular integers $a$ (mod $n$) such that $1\le a\le n$. Here $\varrho(n)=(ϕ(p_1^{ν_1})+1)... (ϕ(p_r^{ν_r})+1)$, where $ϕ(n)$ is the Euler function. In this paper we first summarize some basic properties of regular integers (mod $n$). Then in order to compare the rates of growth of the functions $\varrho(n)$ and $ϕ(n)$ we investigate the average orders and the extremal orders of the functions $\varrho(n)/ϕ(n)$, $ϕ(n)/\varrho(n)$ and $1/\varrho(n)$. | |
| dc.description | 9 pages, final version | |
| dc.identifier | https://arxiv.org/abs/0710.1936 | |
| dc.identifier | http://arxiv.org/abs/0710.1936 | |
| dc.identifier | Annales Univ. Sci. Budapest., Sect. Comp., 29 (2008), 263-275 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/167978 | |
| dc.subject | Number Theory | |
| dc.subject | 11A25, 11N37 | |
| dc.title | Regular integers modulo n | |
| dc.type | text |