# CHARACTERIZING CONGRUENCE PRESERVING FUNCTIONS Z/nZ → Z/mZ VIA RATIONAL POLYNOMIALS

Abstract : 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 $n$.
Document type :
Preprints, Working Papers, ...
Domain :

Cited literature [5 references]

https://hal.archives-ouvertes.fr/hal-01260934
Contributor : Irene Guessarian <>
Submitted on : Monday, January 25, 2016 - 6:08:55 PM
Last modification on : Friday, January 4, 2019 - 5:33:38 PM
Document(s) archivé(s) le : Tuesday, April 26, 2016 - 10:18:14 AM

### Files

CharZnZINTEGERS.pdf
Files produced by the author(s)

### Identifiers

• HAL Id : hal-01260934, version 1

### Citation

Serge Grigorieff, Irene Guessarian, Patrick Cégielski. CHARACTERIZING CONGRUENCE PRESERVING FUNCTIONS Z/nZ → Z/mZ VIA RATIONAL POLYNOMIALS. 2016. ⟨hal-01260934⟩

Record views