Menon’s identity with respect to a generalized divisibility relation

Haukkanen, Pentti

doi:10.1007/s00010-005-2805-7

Cited by 31 publications

(22 citation statements)

References 2 publications

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“…Different Menon-type identities were established by several authors. See, e.g., the papers by Haukkanen [1], Li and Kim, [2,3], Miguel [5], Sita Ramaiah [8], Tȃrnȃuceanu [9], the author [10,11].…”

Section: 2)mentioning

confidence: 99%

Menon-type identities concerning Dirichlet characters

Tóth

2018

Int. J. Number Theory

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Let χ be a Dirichlet character (mod n) with conductor d. In a quite recent paper Zhao and Cao deduced the identity n k=1 (k − 1, n)χ(k) = ϕ(n)τ (n/d), which reduces to Menon's identity if χ is the principal character (mod n). We generalize the above identity by considering even functions (mod n), and offer an alternative approach to proof. We also obtain certain related formulas concerning Ramanujan sums.

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Section: 2)mentioning

confidence: 99%

Menon-type identities concerning Dirichlet characters

Tóth

2018

Int. J. Number Theory

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“…Equation (4.6) is known as Menon's identity, see [21], also [19]. For various choices of S in (4.2) we obtain some analogues of Menon's identity; for example, the analogue presented in [34].…”

Section: P Haukkanen Aemmentioning

confidence: 99%

On a gcd-sum function

Haukkanen

2008

Aequ. math.

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“…Menon [7]. This identity has many generalizations derived by several authors (see, for example, [1][2][3][4][5][6]9,10,[13][14][15][16][17][18][19][20]). A usual technique to prove results of this type is based on the so-called Burnside's lemma (see [8]) concerning group actions.…”

Section: Introductionmentioning

confidence: 95%