On Leonardo Octonions
*Hayrullah ÖzimamoğluCorresponding authorh.ozimamoglu@nevsehir.edu.trDepartments of MathematicsFaculty of Arts and SciencesNevsehir Hacı Bektas Veli UniversityNevsehir, 50300, TurkeyView full profile → , Paula Maria Machado Cruz Catarinopcatarino23@gmail.comDepartment of MathematicsQuinta de PradosUniversity of Trás-os-Montes e Alto DouroVila Real, 5001-801, PortugalView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 05 Jul 2022
- Published Online:
- 04 Sep 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1314
- Pages:
- 2047–2056
Abstract
Keywords
Subject Classifications
References
[1] Y. Alp and E. G. Koçer, “Some properties of Leonardo numbers,” Konuralp Journal of Mathematics, vol. 9, no. 1, pp. 183–189 (2021).
[2] Y. Alp and E. G. Koçer, “Hybrid Leonardo numbers,” Chaos, Solitons & Fractals, vol. 150, 111128 (2021).
[3] P. M. M. C. Catarino and A. Borges, “On Leonardo numbers,” Acta Mathematica Universitatis Comenianae, vol. 89, no. 1, pp. 75–86 (2020).
[4] P. M. M. C. Catarino and A. Borges, “A note on incomplete Leonardo numbers,” Integers, vol. 20, Article #A43 (2020).
[5] O. Keçilioğ̆lu and I. Akkus, “The Fibonacci octonions,” Advances in Applied Clifford Algebras, vol. 25, pp. 151–158 (2015).
[6] T. Koshy, Fibonacci and Lucas Numbers with Applications, Hoboken, NJ, USA: John Wiley & Sons, 2001.
[7] F. Kürüz, A. Dağ̆deviren, and P. M. M. C. Catarino, “On Leonardo Pisano hybrinomials,” Mathematics, vol. 9, no. 22, Article 2923 (2021).
[8] R. Serôdio, “On octonionic polynomials,” Advances in Applied Clifford Algebras, vol. 17, pp. 245–258 (2007).
[9] A. G. Shannon, “A note on generalized Leonardo numbers,” Notes on Number Theory and Discrete Mathematics, vol. 25, no. 3, pp. 97–101 (2019).
[10] Y. Tian, “Matrix representations of octonions and their applications,” Advances in Applied Clifford Algebras, vol. 10, no. 1, pp. 61–90 (2000).
11] S. Vajda, Fibonacci and Lucas Numbers, and the Golden Section: Theory and Applications, New York, NY, USA: Halsted Press (1989).
[12] R. P. M. Vieira, F. R. V. Alves, and P. M. M. C. Catarino, “Relações bidimensionais e identidades da sequência de Leonardo,” Revista Sergipana de Matemática e Educação Matemática, vol. 4, no. 2, pp. 156–173 (2019).
[13] R. P. M. Vieira, M. C. D. S. Mangueira, F. R. V. Alves, and P. M. M. C. Catarino, “Leonardo’s three-dimensional relations and some identities,” Notes on Number Theory and Discrete Mathematics, vol. 27, no. 4, pp. 32–42 (2021).
