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

摘要

Using a simple basis of rational polynomial-like functions P0,...,Pn?1 for the free module of functions Z/nZ → Z/mZ, we characterize the subfamily of congruence preserving functions as the set of linear combinations of the products lcm(k) Pk where lcm(k) is the least common multiple of 2,...,k (viewed in Z/mZ). As a consequence, when n ≥ m, the number of such functions is independent of n.