PORTUGALIAEMATHEMATICA
Vol. 53, No. 3, pp. 331-337 (1996)
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PORTUGALIAE MATHEMATICA Vol. 53, No. 3, pp. 331-337 (1996) |
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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, FIN-33101 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 $$ \sum_{{a\,(\mod n)\atop (a,n)=1}}(a-1,n)=\phi(n)\,\tau(n), $$ 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, $a-1$ 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
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