The Hybrid Numbers of Padovan and Some Identities

Milena Carolina dos Santos Mangueira 1 , Renata Passos Machado Vieira 2 , Francisco Régis Vieira Alves 3 , and Paula Maria Machado Cruz Catarino 4
  • 1 Federal Institute of Ceará Scholarship of Coordination for the Coordination of Superior Level Staff Improvement (CAPES), , Brazil
  • 2 Federal Institute of Ceará, , Brazil
  • 3 Federal Institute of Ceará, Scholarship of National Council for Scientific and Technological Development (CNPq), , Brazil
  • 4 University of Trás-os-Montes and Alto Douro, , Portugal


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.

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