# Multiplicative functions satisfying the functional equation κf(m2+n2) = f(κm2) + f(κn2)

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

## 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  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

• 11A25
• 39B52

### References

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## Cite this paper

Suriyacharoen, W., & Laohakosol, V. (2021). Multiplicative functions satisfying the functional equation κf(m2+n2) = f(κm2) + f(κn2). Notes on Number Theory and Discrete Mathematics, 27(3), 1-11, doi: 10.7546/nntdm.2021.27.3.1-11.