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Multi-extension of arithmetic functions and its applications. (English) Zbl 0921.11006

Let \(f\) be an arithmetic function. The authors define the gcd-extensions of \(f\) (these are arithmetic functions in several variables) and generalize Smith’s determinant. The proofs are elementary.

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
11C20 Matrices, determinants in number theory
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