CHARACTERIZING CONGRUENCE PRESERVING FUNCTIONS Z/nZ → Z/mZ VIA RATIONAL POLYNOMIALS
Résumé
We introduce a basis of rational polynomial-like functions
$P_0,\ldots,P_{n-1}$
for the free module of functions $\Z/n\Z\to\Z/m\Z$.
We then characterize the subfamily
of congruence preserving functions
as the set of linear combinations of the functions $\lcm(k)\,P_k$
where $\lcm(k)$ is the least common multiple of $2,\ldots,k$
(viewed in $\Z/m\Z$).
As a consequence, when $n\geq m$, the number of such functions is independent of $n$.
Domaines
Mathématiques [math]
Origine : Fichiers produits par l'(les) auteur(s)
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