Two generalizations of dual-complex Lucas-balancing numbers

Abstract

In this paper, we study two generalizations of dual-complex Lucas-balancing numbers: dual-complex k-Lucas balancing numbers and dual-complex k-Lucas-balancing numbers. We give some of their properties, among others the Binet formula, Catalan, Cassini, d’Ocagne identities.

Keywords

• lucas-balancing numbers
• diophantine equation
• dual-complex numbers
• binet formula
• catalan identity
• 11b37
• 11b39