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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## Details

### 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*

### Abstract

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.

### Keywords

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

### 2010 Mathematics Subject Classification

- 11A25

### References

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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.