The structure of digraphs associated with the congruence $x^k\equiv y \pmod n$

Title:

The structure of digraphs associated with the congruence $x^k\equiv y \pmod n$

Creator:

Somer, Lawrence

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1960a271-7229-4cd1-aa4b-be01b9db6640
uuid:1960a271-7229-4cd1-aa4b-be01b9db6640

Subject:

Sophie Germain primes, Fermat primes, primitive roots, Chinese Remainder Theorem, congruence, and diagraphs

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We assign to each pair of positive integers $n$ and $k\ge 2$ a digraph $G(n,k)$ whose set of vertices is $H=\{0,1,\dots ,n-1\}$ and for which there is a directed edge from $a\in H$ to $b\in H$ if $a^k\equiv b\pmod n$. We investigate the structure of $G(n,k)$. In particular, upper bounds are given for the longest cycle in $G(n,k)$. We find subdigraphs of $G(n,k)$, called fundamental constituents of $G(n,k)$, for which all trees attached to cycle vertices are isomorphic.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

337-358

Source:

Czechoslovak Mathematical Journal | 2011 Volume:61 | Number:2

Harvested from:

CDK

Metadata only:

false