On k-balancing numbers

Arzu Özkoç and Ahmet Tekcan
Ömür Deveci and Anthony G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 23, 2017, Number 3, Pages 38—52
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Authors and affiliations

Arzu Özkoç
Düzce University, Faculty of Science Department of Mathematics
Konuralp, Düzce, Turkey

Ahmet Tekcan
Uludag University, Faculty of Science Department of Mathematics,
Görukle, Bursa, Turkey


In this work, we consider some algebraic properties of k-balancing numbers. We deduce some formulas for the greatest common divisor of k-balancing numbers, divisibility properties of k-balancing numbers, sums of k-balancing numbers and simple continued fraction expansion of k-balancing numbers.


  • Balancing number
  • Pell number
  • Binary linear recurrences

AMS Classification

  • 11B37
  • 11B39


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Cite this paper

Özkoç, A., & Tekcan, A. (2017). On k-balancing numbers, Notes on Number Theory and Discrete Mathematics, 23(3), 38-52.

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