On polynomial functions from Zn to Zm Original Research Article

We define the concept of a polynomial function from Zn to Zm, which is a generalization of the well-known polynomial function from Zn to Zm. We obtain a necessary and sufficient condition on n and m for all functions from Zn to Zm to be polynomial functions. Then we present canonical representations and the counting formula for the polynomial functions from Zn to Zm. Further, we give an answer to the following problem: How to determine whether a given function from Zn to Zm is a polynomial function, and how to obtain a polynomial to represent a polynomial function?