**Volume 27** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Multiplicative functions satisfying the functional equation κf(m^{2}+n^{2}) = f(κm^{2}) + f(κn^{2})**

*Original research paper. Pages 1–11*

Wuttichai Suriyacharoen and Vichian Laohakosol

Full paper (PDF, 206 Kb) | Abstract

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.

**A short remark on an arithmetic function**

*Original research paper. Pages 12–15*

Anthony G. Shannon and Krassimir T. Atanassov

Full paper (PDF, 154 Kb) | Abstract

*δ*is given. A possible application of it is discussed for representation of the well-known arithmetic functions

*ω*and Kronecker’s delta-function

*δ*.

_{m,s}**On the average order of the gcd-sum function over arbitrary sets of integers**

*Original research paper. Pages 16–28*

V. Siva Rama Prasad and P. Anantha Reddy

Full paper (PDF, 244 Kb) | Abstract

**On Vandiver’s arithmetical function – I**

*Original research paper. Pages 29–38*

József Sándor

Full paper (PDF, 218 Kb) | Abstract

**Note on translated sum on primitive sequences**

*Original research paper. Pages 39–43*

Ilias Laib

Full paper (PDF, 189 Kb) | Abstract

where denotes the set of prime numbers.

**Fibonacci series from power series**

*Original research paper. Pages 44–62*

Kunle Adegoke

Full paper (PDF, 214 Kb) | Abstract

**On some 3 × 3 dimensional matrices associated with generalized Fibonacci numbers**

*Original research paper. Pages 63–72*

Halim Özdemir, Sinan Karakaya and Tuğba Petik

Full paper (PDF, 209 Kb) | Abstract

**A note on ratios of Fibonacci hybrid and Lucas hybrid numbers**

*Original research paper. Pages 73–78*

Emrah Polatlı

Full paper (PDF, 148 Kb) | Abstract

**On evolving chains of cube-free binary sequences**

*Original research paper. Pages 79–94*

Jacek M. Kowalski and Andrzej Pękalski

Full paper (PDF, 217 Kb) | Abstract

**De Moivre-type identities for the Jacobsthal numbers**

*Original research paper. Pages 95–103*

Mücahit Akbiyik and Seda Yamaç Akbiyik

Full paper (PDF, 157 Kb) | Abstract

**Heilbronn-like sums and their properties**

*Original research paper. Pages 104–112*

H. Saydi and M. R. Darafsheh

Full paper (PDF, 227 Kb) | Abstract

**A Diophantine equation about polygonal numbers**

*Original research paper. Pages 113–118*

Yangcheng Li

Full paper (PDF, 206 Kb) | Abstract

has a nonnegative integer solution , then it has infinitely many positive integer solutions of the form , where and , .

**Perron numbers that satisfy Fermat’s equation**

*Original research paper. Pages 119–122*

Pietro Paparella

Full paper (PDF, 146 Kb) | Abstract

*Perron number*such that . It is also shown that there is an aperiodic integer matrix such that .

**A note on the polynomial-exponential Diophantine equation
( a^{n} − 1)(b^{n} − 1) = x^{2}**

*Original research paper. Pages 123–129*

Yasutsugu Fujita and Maohua Le

Full paper (PDF, 186 Kb) | Abstract

**On the rational solutions of y^{2} =x^{3} + k^{6n+3}**

*Original research paper. Pages 130–142*

Richa Sharma and Sanjay Bhatter

Full paper (PDF, 218 Kb) | Abstract

**Arithmetical functions commutable with sums of squares**

*Original research paper. Pages 143–154*

I. Kátai and B. M. Phong

Full paper (PDF, 177 Kb) | Abstract

for every . We also give all arithmetical functions which satisfy the relation

for every , where denotes the set of all positive integers.

**On Ramanujan type identities and Cardano formula**

*Original research paper. Pages 155–174*

Kai Wang

Full paper (PDF, 220 Kb) | Abstract

**Numerical analysis approach to twin primes conjecture**

*Original research paper. Pages 175–183*

Gabriele Di Pietro

Full paper (PDF, 194 Kb) | Abstract

**Pauli–Fibonacci quaternions**

*Original research paper. Pages 184–193*

Fügen Torunbalcı Aydın

Full paper (PDF, 177 Kb) | Abstract

**Book review: “Arithmetic Functions”**

*Book review. Pages 194–195*

Anthony Greville Shannon

Book review (PDF, 318 Kb)

*This issue of the International Journal “Notes on Number Theory and Discrete Mathematics” is published with the financial support of the Bulgarian National Science Fund, Grant Ref. No. KP-06-NP2/26/2020.*