An identical equation for arithmetic functions of several variables and applications

Vichian Laohakosol and Pinthira Tangsupphathawat
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 24, 2018, Number 4, Pages 11—17
DOI: 10.7546/nntdm.2018.24.4.11-17
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Authors and affiliations

Vichian Laohakosol
Department of Mathematics, Faculty of Science
Kasetsart University, Bangkok 10900, Thailand

Pinthira Tangsupphathawat
Department of Mathematics, Faculty of Science and Technology
Phranakorn Rajabhat University, Bangkok 10220, Thailand


An identical equation for arithmetic functions is proved generalizing the 2-variable case due to Venkataraman. It is then applied to characterize multiplicative functions which are variable-separated, and to deduce interesting properties of generalized Ramanujan sums.


  • Arithmetic function of several variables
  • Identical equation
  • Multiplicative functions
  • Completely multiplicative functions

2010 Mathematics Subject Classification

  • 11A25


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Cite this paper

Laohakosol, V., & Tangsupphathawat, P. (2018). An identical equation for arithmetic functions of several variables and applications. Notes on Number Theory and Discrete Mathematics, 24(4), 11-17, doi: 10.7546/nntdm.2018.24.4.11-17.

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