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

Selin Sarı and Gül Karadeniz-Gözeri

Journal of Mathematics, 2025, vol. 2025, 1-12

Abstract: 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 Bm-subbalancing numbers as the solutions of these Diophantine equations. Moreover, we especially consider B3-subbalancing numbers and obtain various algebraic identities regarding these numbers. Furthermore, we derive some results on the relationship between B3-subbalancing and b3-subbalancing numbers.

Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jjmath:2173041

DOI: 10.1155/jom/2173041

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