Research Article
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Year 2021, , 226 - 233, 31.12.2021
https://doi.org/10.47000/tjmcs.780474

Abstract

References

  • [1] Akkus, I., Kecilioglu, O., Split Fibonacci and Lucas Octonions, Adv. Appl. Clifford Algebras, 25(2015), 517–525.
  • [2] Akyiğit, M., Kösal, H.H., Tosun, M., Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24(2014), 631–641.
  • [3] Catarino, P., The Modified Pell and The Modified k-Pell Quaternions and Octonions, Adv. Appl. Clifford Algebras, 26(2)(2016), 577–590.
  • [4] Cimen, C.B., İpek, A., On Pell Quaternions and Pell-Lucas Quaternions, Adv. Appl. Clifford Algebras, 26(2016), 39–51.
  • [5] Flaut, C., Stefanescu, M., Some Equations over Generalized Quaternion and Octonion Division Algebras, Bull. Math. Soc. Sci. Math. Roum., 52(100)(4)(2009), 427–439.
  • [6] Halici, S., On Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 22(2012), 321–327.
  • [7] Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70(1963), 289–291.
  • [8] Horadam, A.F., Quaternion Recurrence Relations, Ulam Quarterly, 2(1993), 23–33.
  • [9] Iakin, A.L., Generalized Quaternions of Higher Order, Fibonacci Quart, 15(1977), 343–346.
  • [10] Iyer, M.R., A Note on Fibonacci Quaternions, Fibonacci Quart, 3(1969), 225–229.
  • [11] Keçilioğlu, O., Akkus, I., The Fibonacci Octonions, Adv. Appl. Clifford Algebras, 25(2015), 151–158.
  • [12] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, 2001.
  • [13] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • [14] Ramirez, J.L., Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. St. Univ. Ovidius Constanta, 23(2)(2015), 201–212.
  • [15] Savin, D., Some Properties of Fibonacci numbers, Fibonacci Octonions, and generalized Fibonacci-Lucas Octonions, Adv. Difference Equ., 2015.1(2015), 298.
  • [16] Swamy, M.N.S., On Generalized Fibonacci Quaternions, The Fib. Quarterly, 5(1973), 547–550.
  • [17] Szynal-Liana, A., Wloch, I., The Pell Quaternions and The Pell Octonions, Adv. Appl. Clifford Algebras, 26(2016), 435–440

On Pell and Pell-Lucas Generalized Octonions

Year 2021, , 226 - 233, 31.12.2021
https://doi.org/10.47000/tjmcs.780474

Abstract

In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra $\mathbb{O}(a,b,c)$ where $a,b$ and $c$ are real numbers. For these number sequences, we obtain Binet formulas and gave some well-known identities such as Catalan's identity, Cassini's identity and d'Ocagne's identity.

References

  • [1] Akkus, I., Kecilioglu, O., Split Fibonacci and Lucas Octonions, Adv. Appl. Clifford Algebras, 25(2015), 517–525.
  • [2] Akyiğit, M., Kösal, H.H., Tosun, M., Fibonacci Generalized Quaternions, Adv. Appl. Clifford Algebras, 24(2014), 631–641.
  • [3] Catarino, P., The Modified Pell and The Modified k-Pell Quaternions and Octonions, Adv. Appl. Clifford Algebras, 26(2)(2016), 577–590.
  • [4] Cimen, C.B., İpek, A., On Pell Quaternions and Pell-Lucas Quaternions, Adv. Appl. Clifford Algebras, 26(2016), 39–51.
  • [5] Flaut, C., Stefanescu, M., Some Equations over Generalized Quaternion and Octonion Division Algebras, Bull. Math. Soc. Sci. Math. Roum., 52(100)(4)(2009), 427–439.
  • [6] Halici, S., On Fibonacci Quaternions, Adv. Appl. Clifford Algebras, 22(2012), 321–327.
  • [7] Horadam, A.F., Complex Fibonacci Numbers and Fibonacci Quaternions, Amer. Math. Monthly, 70(1963), 289–291.
  • [8] Horadam, A.F., Quaternion Recurrence Relations, Ulam Quarterly, 2(1993), 23–33.
  • [9] Iakin, A.L., Generalized Quaternions of Higher Order, Fibonacci Quart, 15(1977), 343–346.
  • [10] Iyer, M.R., A Note on Fibonacci Quaternions, Fibonacci Quart, 3(1969), 225–229.
  • [11] Keçilioğlu, O., Akkus, I., The Fibonacci Octonions, Adv. Appl. Clifford Algebras, 25(2015), 151–158.
  • [12] Koshy, T., Fibonacci and Lucas Numbers with Applications, A Wiley-Interscience Publication, Canada, 2001.
  • [13] Koshy, T., Pell and Pell-Lucas Numbers with Applications, Springer, New York, 2014.
  • [14] Ramirez, J.L., Some Combinatorial Properties of the k-Fibonacci and the k-Lucas Quaternions, An. St. Univ. Ovidius Constanta, 23(2)(2015), 201–212.
  • [15] Savin, D., Some Properties of Fibonacci numbers, Fibonacci Octonions, and generalized Fibonacci-Lucas Octonions, Adv. Difference Equ., 2015.1(2015), 298.
  • [16] Swamy, M.N.S., On Generalized Fibonacci Quaternions, The Fib. Quarterly, 5(1973), 547–550.
  • [17] Szynal-Liana, A., Wloch, I., The Pell Quaternions and The Pell Octonions, Adv. Appl. Clifford Algebras, 26(2016), 435–440
There are 17 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences, Engineering
Journal Section Articles
Authors

Ümit Tokeşer 0000-0003-4773-8291

Tuğba Mert 0000-0001-8258-8298

Zafer Ünal 0000-0003-2445-1028

Göksal Bilgici 0000-0001-9964-5578

Publication Date December 31, 2021
Published in Issue Year 2021

Cite

APA Tokeşer, Ü., Mert, T., Ünal, Z., Bilgici, G. (2021). On Pell and Pell-Lucas Generalized Octonions. Turkish Journal of Mathematics and Computer Science, 13(2), 226-233. https://doi.org/10.47000/tjmcs.780474
AMA Tokeşer Ü, Mert T, Ünal Z, Bilgici G. On Pell and Pell-Lucas Generalized Octonions. TJMCS. December 2021;13(2):226-233. doi:10.47000/tjmcs.780474
Chicago Tokeşer, Ümit, Tuğba Mert, Zafer Ünal, and Göksal Bilgici. “On Pell and Pell-Lucas Generalized Octonions”. Turkish Journal of Mathematics and Computer Science 13, no. 2 (December 2021): 226-33. https://doi.org/10.47000/tjmcs.780474.
EndNote Tokeşer Ü, Mert T, Ünal Z, Bilgici G (December 1, 2021) On Pell and Pell-Lucas Generalized Octonions. Turkish Journal of Mathematics and Computer Science 13 2 226–233.
IEEE Ü. Tokeşer, T. Mert, Z. Ünal, and G. Bilgici, “On Pell and Pell-Lucas Generalized Octonions”, TJMCS, vol. 13, no. 2, pp. 226–233, 2021, doi: 10.47000/tjmcs.780474.
ISNAD Tokeşer, Ümit et al. “On Pell and Pell-Lucas Generalized Octonions”. Turkish Journal of Mathematics and Computer Science 13/2 (December 2021), 226-233. https://doi.org/10.47000/tjmcs.780474.
JAMA Tokeşer Ü, Mert T, Ünal Z, Bilgici G. On Pell and Pell-Lucas Generalized Octonions. TJMCS. 2021;13:226–233.
MLA Tokeşer, Ümit et al. “On Pell and Pell-Lucas Generalized Octonions”. Turkish Journal of Mathematics and Computer Science, vol. 13, no. 2, 2021, pp. 226-33, doi:10.47000/tjmcs.780474.
Vancouver Tokeşer Ü, Mert T, Ünal Z, Bilgici G. On Pell and Pell-Lucas Generalized Octonions. TJMCS. 2021;13(2):226-33.