Cobalancing hybrid numbers

Mariola Rubajczyk, Anetta Szynal-Liana

Abstract


Hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper, we define and study hybrid numbers with cobalancing and Lucas-cobalancing coefficients. We derive some fundamental identities for these numbers, among others the Binet formulas and the general bilinear index-reduction formulas which imply the Catalan, Cassini, Vajda, d’Ocagne and Halton identities. Moreover, the generating functions for cobalancing and Lucas-cobalancing hybrid numbers are presented.

Keywords


Cobalancing numbers; Diophantine equation; hybrid numbers; Binet formula

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References


Behera, A., Panda, G. K., On the square roots of triangular numbers, Fibonacci Quart. 37(2) (1999), 98–105.

Bród, D., Szynal-Liana, A., Włoch, I., Balancing hybrid numbers, their properties and some identities, Indian J. Math. 63(1) (2021), 143–157.

Ozdemir, M., Introduction to Hybrid Numbers, Adv. Appl. Clifford Algebr. 28(1) (2018), Paper No. 11, 32 pp.

Ozkoc, A., Tridiagonal matrices via k-balancing number, British Journal of Mathematics & Computer Science 10(4) (2015), 1–11.

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

Panda, G. K., Some fascinating properties of balancing numbers, in: Proceedings of the Eleventh International Conference on Fibonacci Numbers and their Applications, 185–189, Cong. Numerantium 194 (2009).

Panda, G. K., Ray, P. K., Cobalancing numbers and cobalancers, International Journal of Mathematics and Mathematical Sciences 8 (2005), 1189–1200.

Panda, G. K., Ray, P. K., Some links of balancing and cobalancing numbers with Pell and associated Pell numbers, Bull. Inst. Math. Acad. Sin. (N.S.) 6(1) (2011), 41–72.

Polatlı, E., Hybrid numbers with Fibonacci and Lucas hybrid number coefficients, Universal Journal of Mathematics and Applications 6(3) (2023), 106–113.

Szynal-Liana A., Włoch I., On Pell and Pell–Lucas hybrid numbers, Comment. Math. 56(1–2) (2018), 11–17.




DOI: http://dx.doi.org/10.17951/a.2024.78.1.87-95
Date of publication: 2024-07-29 22:47:27
Date of submission: 2024-07-11 14:43:33


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