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A generalization of the Smarandache function to several variables. (English) Zbl 1114.11003
Let \(G_d(\mathbb Z_n)\) denote the ring of polynomial functions in \(d\) variables defined over \(\mathbb Z_n\) with values in \(\mathbb Z_n\). This paper characterizes those functions \(f:\mathbb Z_n^d \to \mathbb Z_n\) which belong to \(G_d(\mathbb Z_n)\) and evaluates the number of elements of the ring \(G_d(\mathbb Z_n)\).

MSC:
11A25 Arithmetic functions; related numbers; inversion formulas
11C08 Polynomials in number theory
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