On subbalancing numbers involving the third balancing number in the Diophantine equation

Abstract

In this paper, we consider subbalancing numbers formed by using the third balancing number in the Diophantine equation. We obtain some algebraic identities on these numbers which are also known as B3-subbalancing numbers. We provide a variety of sum formulas and some divisibility properties associated with these numbers. We also give several Pythagorean triples obtained by using B3-subbalancing numbers. Furthermore, we derive some functions that takes B3-subbalancing and balancing numbers values for B3-subbalancing number arguments.