PORTUGALIAE MATHEMATICA Vol. 53, No. 3, pp. 331337 (1996) 

A Generalization of Menon's Identity with Respect to a Set of PolynomialsPentti Haukkanen and Jun WangDepartment of Mathematical Sciences, University of Tampere,P.O. Box 607, FIN33101 Tampere  FINLAND Institute of Mathematical Sciences, Dalian University of Technology, Dalian 116024  PEOPLE'S REPUBLIC OF CHINA Abstract: P. Kesava Menon's elegant identity states that $$ \sum_{{a\,(\mod n)\atop (a,n)=1}}(a1,n)=\phi(n)\,\tau(n), $$ where $\phi(n)$ is Euler's totient function and $\tau(n)$ is the number of divisors of $n$. In this paper we generalize this identity so that, among other things, $a1$ is replaced with a set $\{f_{i}(\bfc{a})\}$ of polynomials in $\Z[a_{1},a_{2},...,a_{u}]$. Keywords: Menon's identity; set of polynomials; Euler's totient; Jordan's totient; regular arithmetical convolution. Classification (MSC2000): 11A25 Full text of the article:
Electronic version published on: 29 Mar 2001. This page was last modified: 27 Nov 2007.
© 1996 Sociedade Portuguesa de Matemática
