On bicomplex Pell and Pell-Lucas numbers
Fugen Torunbalci Aydin
TL;DR
This paper introduces bicomplex Pell and Pell-Lucas numbers, explores their algebraic properties, and derives identities like Binet's, Cassini's, and Catalan's, extending classical number theory into bicomplex number systems.
Contribution
It defines new bicomplex Pell and Pell-Lucas numbers and establishes their fundamental properties and identities, expanding the scope of classical Pell number theory.
Findings
Derived algebraic properties of bicomplex Pell numbers
Established identities such as Binet's, Cassini's, and Catalan's for these numbers
Connected bicomplex Pell numbers with classical Pell and Pell-Lucas numbers
Abstract
In this paper, bicomplex Pell and bicomplex Pell-Lucas numbers are defined. Also, negabicomplex Pell and negabicomplex Pell-Lucas numbers are given. Some algebraic properties of bicomplex Pell and bicomplex Pell-Lucas numbers which are connected with bicomplex numbers and Pell and Pell-Lucas numbers are investigated. Furthermore, d'Ocagne's identity, Binet's formula, Cassini's identity and Catalan's identity for these numbers are given.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Mathematical Inequalities and Applications · Advanced Mathematical Identities