The ring of polyfunctions over Z/nZ

We study the ring of polyfunctions over Z/nZ. The a commutative R with unit element is functions f:R→R which admit polynomial representative p∈R[x] in sense that f(x)=p(x) for all x∈R. This allows to define invariant s associates value N∪{∞}. function generalizes number theoretic Smarandache function. For R=Z/nZ we provide unique representation polynomials vanish as yields new formula Ψ(n) also investigate algebraic properties In particular, identify additive subgroup and structure itself. Moreover derive formulas size several variables Z/nZ, compute are units ring.