**Volume 29** ▶ Number 1 ▷ Number 2 ▷ Number 3 ▷ Number 4

**Quotients of arithmetical functions under the Dirichlet convolution**

*Original research paper. Pages 185–194*

Pentti Haukkanen

Full paper (PDF, 189 Kb) | Abstract

**A note on telephone numbers and their matrix generators**

*Original research paper. Pages 195–203*

Francisco Regis Vieira Alves, Renata Passos Machado Vieira and Paula Maria Machado Cruz Catarino

Full paper (PDF, 150 Kb) | Abstract

**Some identities involving Chebyshev polynomials, Fibonacci polynomials and their derivatives**

*Original research paper. Pages 204–215*

Jugal Kishore and Vipin Verma

Full paper (PDF, 186 Kb) | Abstract

**Some new relations between T(a_{1},a_{2},a_{3},a_{4},a_{5}; n) and N(a_{1},a_{2},a_{3},a_{4},a_{5}; n)**

*Original research paper. Pages 216–225*

Vandna and Mandeep Kaur

Full paper (PDF, 181 Kb) | Abstract

**The quaternion-type cyclic-Fibonacci sequences in groups**

*Original research paper. Pages 226–240*

Nazmiye Yilmaz, Esra Kırmızı Çetinalp and Ömür Deveci

Full paper (PDF, 267 Kb) | Abstract

*m*and the generating matrices of these sequences. Finally, we introduce the quaternion-type cyclic-Fibonacci sequences in finite groups. We calculate the lengths of periods for these sequences of the generalized quaternion groups and obtain quaternion-type cyclic-Fibonacci orbits of the quaternion groups

*Q*

_{8}and

*Q*

_{16}as applications of the results.

**Representations of positive integers as sums of arithmetic progressions, I**

*Original research paper. Pages 241–259*

Chungwu Ho, Tian-Xiao He and Peter J.-S. Shiue

Full paper (PDF, 267 Kb) | Abstract

**Representations of positive integers as sums of arithmetic progressions, II**

*Original research paper. Pages 260–275*

Chungwu Ho, Tian-Xiao He and Peter J.-S. Shiue

Full paper (PDF, 265 Kb) | Abstract

**New properties of divisors of natural number**

*Original research paper. Pages 276–283*

Hamilton Brito da Silva

Full paper (PDF, 298 Kb) | Abstract

**A class of solutions of the equation d(n^{2}) = d(φ(n))**

*Original research paper. Pages 284–309*

Zahra Amroune, Djamel Bellaouar and Abdelmadjid Boudaoud

Full paper (PDF, 309 Kb) | Abstract

**Unrestricted Tribonacci and Tribonacci–Lucas quaternions**

*Original research paper. Pages 310–321*

Gonca Kızılaslan and Leyla Karabulut

Full paper (PDF, 287 Kb) | Abstract

**On the k-Fibonacci and k-Lucas spinors**

*Original research paper. Pages 322–335*

Munesh Kumari, Kalika Prasad and Robert Frontczak

Full paper (PDF, 285 Kb) | Abstract

*k*-Fibonacci and

*k*-Lucas spinors. Starting with the Binet formulas we present their basic properties, such as Cassini’s identity, Catalan’s identity, d’Ocagne’s identity, Vajda’s identity, and Honsberger’s identity. In addition, we discuss their generating functions. Finally, we obtain sum formulae and relations between

*k*-Fibonacci and

*k*-Lucas spinors.

*p*-Analogue of biperiodic Pell and Pell–Lucas polynomials

*Original research paper. Pages 336–347*

Bahar Kuloğlu, Engin Özkan and Anthony G. Shannon

Full paper (PDF, 944 Kb) | Abstract

*p*-analogue Pell and Pell–Lucas polynomials are established and the generating functions of these new polynomials are obtained. Some theorems and propositions depending on the generating functions are also expressed. Then, by association with these, the polynomials of so-called ‘incomplete’ number sequences have been obtained, and elegant summation relations provided. The paper has also been placed in the appropriate historical context for ease of further development.

**On the multiplicative group generated by . V **

*Original research paper. Pages 348–353*

I. Kátai and B. M. Phong

Full paper (PDF, 291 Kb) | Abstract

Then

**Intersection of Padovan and Tribonacci sequences**

*Original research paper. Pages 354–359*

Nurretin Irmak and Abdullah Açikel

Full paper (PDF, 276 Kb) | Abstract

**Recurrence relations connecting mock theta functions and restricted partition functions**

*Original research paper. Pages 360–371*

M. Rana, H. Kaur and K. Garg

Full paper (PDF, 234 Kb) | Abstract

**A note on the length of some finite continued fractions**

*Original research paper. Pages 372–377*

Khalil Ayadi and Chiheb Ben Bechir

Full paper (PDF, 225 Kb) | Abstract

**On certain arithmetical functions of exponents in the factorization of integers**

*Original research paper. Pages 378–388*

József Sándor and Krassimir T. Atanassov

Full paper (PDF, 246 Kb) | Abstract

**Hyperbolic Horadam hybrid functions**

*Original research paper. Pages 389–401*

Efruz Özlem Mersin

Full paper (PDF, 213 Kb) | Abstract

**A note on generating primitive Pythagorean triples using matrices**

*Original research paper. Pages 402–406*

Jathan Austin

Full paper (PDF, 145 Kb) | Abstract

*This volume 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-NP4/30/2022.*