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