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A generalization of Menon’s identity with respect to a set of polynomials. (English) Zbl 0856.11006

Kesava Menon established the interesting identity \[ \sum_{\substack{ a\bmod n\\ (a, n)=1 }} (a-1, n)= \varphi (n) \tau (n). \] The authors generalize this to several variables and polynomials with integer coefficients instead of \(a-1\).

MSC:

11A25 Arithmetic functions; related numbers; inversion formulas
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