Wuttichai Suriyacharoen and Vichian Laohakosol

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 27, 2021, Number 3, Pages 1–11

DOI: 10.7546/nntdm.2021.27.3.1-11

**Full paper (PDF, 206 Kb)**

## Details

### Authors and affiliations

Wuttichai Suriyacharoen

*Department of Mathematics and Statistics, Thammasat University
99 Moo 18 Paholyothin Rd, Klong Nueng, Klong Luang, Pathumthani 12121, Thailand
*

Vichian Laohakosol

*Department of Mathematics, Kasetsart University
50 Ngamwongwan Rd, Chatuchak, Bangkok 10900, Thailand
*

### Abstract

For a fixed positive integer , the functional equation

is solved for multiplicative functions . This complements a 1996 result of Chung [2] which deals with the case . The method used relies on the sum of two squares theorem in number theory.

### Keywords

- Arithmetic function
- Multiplicative function
- Functional equation
- Sum of squares

### 2020 Mathematics Subject Classification

- 11A25
- 39B52

### References

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## Cite this paper

Suriyacharoen, W., & Laohakosol, V. (2021). Multiplicative functions satisfying the functional equation *κf*(*m*^{2}+*n*^{2}) = *f*(*κm*^{2}) + *f*(*κn*^{2}). *Notes on Number Theory and Discrete Mathematics*, 27(3), 1-11, DOI: 10.7546/nntdm.2021.27.3.1-11.