The Hybrid Numbers of Padovan and Some Identities

• Autorzy: Milena Carolina dos Santos Mangueira , Renata Passos Machado Vieira , Francisco Régis Vieira Alves , Paula Maria Machado Cruz Catarino
• Języki publikacji: EN

Abstrakty

EN

In this article, we will define Padovan's hybrid numbers, based on the new noncommutative numbering system studied by Özdemir ([7]). Such a system that is a set involving complex, hyperbolic and dual numbers. In addition, Padovan's hybrid numbers are created by combining this set, satisfying the relation ih = -hi = ɛ + i. Given this, some properties and identities are shown for these numbers, such as Binet's formula, generating matrix, characteristic equation, norm, and generating function. In addition, these numbers are extended to the integer field and some identities are made. (original abstract)

Słowa kluczowe

EN

Mathematics; Number theory; Matrix

PL

Matematyka; Teoria liczb; Macierze

• Czasopismo: Annales Mathematicae Silesianae
• Rocznik: 2020
• Tom: 34 (2)
• Strony: 256--267

Twórcy

autor

Milena Carolina dos Santos Mangueira

• Federal University of Ceará, Brasil

autor

Renata Passos Machado Vieira

• Federal University of Ceará, Brasil

autor

Francisco Régis Vieira Alves

• Federal University of Ceará, Brasil

autor

Paula Maria Machado Cruz Catarino

• University of Trás-os-Montes and Alto Douro, Portugal

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Identyfikatory

DOI

10.2478/amsil-2020-0019