Geodesic
The structure of digraphs associated with the congruence $x^k\equiv y \pmod n$
Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 337-358 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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.
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.
DOI : 10.1007/s10587-011-0079-x
Classification : 05C20, 11A07, 11A15, 20K01
Keywords: Sophie Germain primes; Fermat primes; primitive roots; Chinese Remainder Theorem; congruence; digraphs 
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     title = {The structure of digraphs associated with the congruence $x^k\equiv y \pmod n$},
     journal = {Czechoslovak Mathematical Journal},
     pages = {337--358},
     year = {2011},
     volume = {61},
     number = {2},
     doi = {10.1007/s10587-011-0079-x},
     mrnumber = {2905408},
     zbl = {1249.11006},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0079-x/}
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Somer, Lawrence; Křížek, Michal. The structure of digraphs associated with the congruence $x^k\equiv y \pmod n$. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 2, pp. 337-358. doi: 10.1007/s10587-011-0079-x

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