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

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  • Selin Sarı
  • Gül Karadeniz-Gözeri

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.

Suggested Citation

  • Selin Sarı & Gül Karadeniz-Gözeri, 2025. "On the Existence of Solutions of Diophantine Equations Related to Subbalancing Numbers," Journal of Mathematics, Hindawi, vol. 2025, pages 1-12, July.
    • Handle: RePEc:hin:jjmath:2173041
    DOI: 10.1155/jom/2173041
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