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aequationes mathematicae

, Volume 70, Issue 3, pp 240–246 | Cite as

Menon’s identity with respect to a generalized divisibility relation

  • Pentti Haukkanen
Research paper

Summary.

We present a generalization of P. Kesava Menon’s identity
$$ {\sum\limits_{\scriptstyle a{\left( {\bmod {\rm{ }}n} \right)} \hfill \atop \scriptstyle (a,n) = 1 \hfill} {{\left( {a - 1,n} \right)} = \phi {\left( n \right)}\tau {\left( n \right)},} } $$
where ϕ(n) is Euler’s totient function and τ(n) is the number of positive divisors of n. As special cases of the generalized identity we also obtain the analogues of Menon’s identity with respect to the exponentially binary and ternary divisibility relations.

Mathematics Subject Classification (2000).

11A25 

Keywords.

Arithmetical sums Menon’s identity Euler’s totient function 

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Copyright information

© Birkhäuser Verlag, Basel 2005

Authors and Affiliations

  1. 1.Department of Mathematics Statistics and PhilosophyUniversity of TampereTampereFinland

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