CHARACTERIZING CONGRUENCE PRESERVING FUNCTIONS Z/nZ → Z/mZ VIA RATIONAL POLYNOMIALS
نویسندگان
چکیده
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.
منابع مشابه
Characterizing congruence preserving functions $Z/nZ\to Z/mZ$ via rational polynomials
We introduce a basis of rational polynomial-like functions P 0 ,. .. , P n−1 for the free module of functions Z/nZ → Z/mZ. 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,. .. , k (viewed in Z/mZ). As a consequence , when n ≥ m, the number of such functions is indep...
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