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

2024    Karadeniz-Gözeri, G.; Sarı, S.

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 $B_3$-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 $B_3$-subbalancing numbers. Furthermore, we derive some functions that takes $B_3$-subbalancing and balancing numbers values for $B_3$-subbalancing number arguments.