Abstract:In the present work, we define harmonic complex balancing numbers by considering well-known balancing numbers and inspiring harmonic numbers. Mainly, we investigate some of their basic characteristic properties such as the Binet formula and Cassini identity, etc. In addition, one type of symmetric matrix family whose entries are harmonic complex balancing numbers is constructed. Additionally, some linear algebraic properties are obtained. Furthermore, some inequalities are stated by exploiting the well-known i… Show more
In this work, supercobalancing numbers are considered and some properties of these numbers are investigated. In the first part of this work, it is shown that every supercobalancing number is also a subbalancer. More specifically, B3-supercobalancing numbers which have not been considered before within the scope of this subject are examined. All the solution classes of the Diophantine equation of B3-supercobalancing numbers are determined exactly.
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