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

Sarı S., KARADENİZ GÖZERİ G.

Journal of Mathematics, cilt.2025, sa.1, 2025 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 2025 Sayı: 1
  • Basım Tarihi: 2025
  • Doi Numarası: 10.1155/jom/2173041
  • Dergi Adı: Journal of Mathematics
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Anahtar Kelimeler: balancing numbers, Binet formula, Diophantine equation, recurrence relation, subbalancing numbers
  • İstanbul Üniversitesi Adresli: Evet

Özet

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.