A New Class of Leonardo Hybrid Numbers and Some Remarks on Leonardo Quaternions over Finite Fields

Elif Tan (), Diana Savin and Semih Yılmaz
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Elif Tan: Department of Mathematics, Faculty of Science, Ankara University, 06100 Ankara, Turkey
Diana Savin: Department of Mathematics and Computer Science, Transilvania University of Brasov, 500091 Brasov, Romania
Semih Yılmaz: Department of Actuarial Sciences, Kırıkkale University, 71450 Kırıkkale, Turkey

Mathematics, 2023, vol. 11, issue 22, 1-14

Abstract: In this paper, we present a new class of Leonardo hybrid numbers that incorporate quantum integers into their components. This advancement presents a broader generalization of the q -Leonardo hybrid numbers. We explore some fundamental properties associated with these numbers. Moreover, we study special Leonardo quaternions over finite fields. In particular, we determine the Leonardo quaternions that are zero divisors or invertible elements in the quaternion algebra over the finite field Z p for special values of prime integer p .

Keywords: hybrid numbers; quaternions; Fibonacci numbers; Leonardo numbers; quantum integer; zero divisor; finite fields (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
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