Generalized Balancing and Balancing-Lucas numbers
DOI:
https://doi.org/10.22199/issn.0717-6279-5712Keywords:
Balancing numbers, balancing-Lucas numbers, generalized Balancing numbers, generalized balancing-Lucas numbers, generating functions, Binet formulaAbstract
In this paper, we introduce a generalization of Balancing and Balancing-Lucas numbers. We describe some of their properties also we give the related matrix representation and divisibility properties.
References
A. Al-Kateeb, A generalization of Jacobsthal and Jacobsthal-Lucas numbers, JJMS, Vol. 14 (3), pp. 467-481, 2021.
U. K. Dutta, P. K. Ray, On arithmetic functions of balancing and Lucas-balancing numbers, Math. Commun., Vol. 24, pp. 77-81, 2019.
S. Falcon, A.Plaza, On the Fibonacci k-numbers, Chaos, Solitons and Fractals, Vol. 32 No. 5, pp. 1615-1624, 2007.
L. Trojnar-Spelina and I. Wloch, On generalized Pell and Pell-Lucas numbers. Iran J. Sci Technol Trans Sci, Vol. 43, pp. 2871-2877, 2019.
G. K. Panda, Some fascinating properties of balancing numbers, Proceedings of the Eleventh International Conference on Fibonacci Numbers and Their Applications, (Willian Webb, Ed.), Vol. 194, 2009.
D. Tasci, Gaussian balancing and Gaussin balancing-Lucas numbers, Journal of Science and Arts, No. 3 (44), pp.661-666, 2018.
A. Patra, G. K. Panda, T. Khemaratchatakumthorn, Exact divisibility by powers of the balancing and Lucas-balancing numbers, Fibonacci Quart., Vol. 59, pp. 57-64, 2021.
P. K. Ray, Balancing and Lucas-balancing sums by matrix methods. Mathematical Reports, Vol. 17 (2), 2015.
P. K. Ray, On the properties of k-balancing and k-Lucas-balancing numbers. Acta Comment. Univ. Tartu. Math., Vol. 21, pp. 259-274, 2017.
K. Rosen, Elementary Number Theory and its Applications, AddisonWesley Comp. Sixth Edition, 2011.
M. K. Sahukar and G. K. Panda, Arithmetic functions of balancing numbers, The Fibonacci Quarterly, Vol. 56, pp. 246-251, 2018.
Tekcan, A., Tayat, M. and Ozbek, M. The Diophantine Equation 8x2 + y2 + 8x(1 + t) + (2t + 1)2 = 0 and t-Balancing Numbers. ISR Combinatorics, 2014.
F. Yilmaz and D. Bozkurt, The generalized order-k Jacobsthal numbers, Int. J. Contemp. Math. Sciences, Vol. 4 No. 34, pp. 1685-1694, 2009.
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Copyright (c) 2024 Alaa Al-Kateeb, Hasan Al-Zoubi
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