On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers

In this paper, we introduce a new sequence of subbalancing numbers by considering balancing numbers as the values of D in the Diophantine equations provided by subbalancing numbers. For this, first we prove that when the values of the positive integer D are chosen as balancing numbers, there exist integer solutions of the Diophantine equations that correspond to these values of D . Then, we obtain the sequence of B m ‐subbalancing numbers as the solutions of these Diophantine equations. Moreover, we especially consider B 3 ‐subbalancing numbers and obtain various algebraic identities regarding these numbers. Furthermore, we derive some results on the relationship between B 3 ‐subbalancing and b 3 ‐subbalancing numbers.