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Journals / Turkish Journal of Mathematics and Computer Science / 2021 / Cilt: 13 - Sayı: 2

On Pell and Pell-Lucas Generalized Octonions

Göksal Bilgici
Zafer ÜNAL
Tuğba MERT
Ümit TOKEŞER
Pages
226–233
Publication Date
2022-11-05
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

For these number sequences, we obtain Binet formulas and gave some wellknown identities such as Catalan’s identity, Cassini’s identity and d’Ocagne’s identity.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra O(a, b, c) where a, b and c are real numbers.
📊
Key Findings & Data:In this study, we gave a generalization on Pell and Pell-Lucas octonions over the algebra O(a, b, c) where a, b and c are real numbers.
💡
Conclusion & Impact:For these number sequences, we obtain Binet formulas and gave some wellknown identities such as Catalan’s identity, Cassini’s identity and d’Ocagne’s identity.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

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

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Cite This Article

Bilgici, G., ÜNAL, Z., MERT, T., TOKEŞER, Ü. (2022). On Pell and Pell-Lucas Generalized Octonions. Turkish Journal of Mathematics and Computer Science, Cilt: 13 - Sayı: 2, 226–233. https://ajindex.com/articles/609084

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References (17)

  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