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

Haukkanen, P.; Wang, J.

Port. Math. 53, No. 3, 331-337 (1996).

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 \(a-1\).

Reviewer: J.Spilker (Freiburg i.Br.)

MSC:

11A25

Arithmetic functions; related numbers; inversion formulas

Keywords:

generalization of Menon’s identity; arithmetical functions