Exploring novel Fermat polynomials and their transformative properties
*Bahar KuloğluCorresponding authorbkuloglu@sivas.edu.trbahar_kuloglu@hotmail.comDepartment of Engineering Basic SciencesSivas University of Science and TechnologySivas, Türkiye0000-0001-7624-8270View full profile → , Engin Eserengineser1978@gmail.comDepartment of MathematicsFaculty of Art and SciencesErzincan Binali Yıldırım UniversityErzincan, Türkiye0000-0001-5965-4162View full profile → , Engin Özkanengin.ozkan@marmara.edu.trDepartment of MathematicsMarmara Universityİstanbul, Türkiye0000-0002-4188-7248View full profile →
* Corresponding author · click or hover a name for details
- Received:
- 08 May 2024
- Published Online:
- 18 Nov 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIOS-1811
- Pages:
- 1011–1026
Abstract
Keywords
Subject Classifications
References
[1] E. Özkan and B. Kuloğlu, “On the new Narayana polynomials, the Gauss Narayana numbers and their polynomials,” Asian-European Journal of Mathematics, vol. 14, no. 06, p. 2150100 (2021).
[2] V. E. Hoggatt Jr., Fibonacci and Lucas Numbers. Santa Clara, CA: The Fibonacci Association, University of Santa Clara (1969).
[3] T. Koshy, Fibonacci and Lucas Numbers with Applications, vol. 2. Hoboken, NJ: John Wiley & Sons (2019).
[4] W. M. Abd-Elhameed and Y. H. Youssri, “Solutions of the connection problems between Fermat and generalized Fibonacci polynomials,” JP Journal of Algebra, Number Theory and Applications, vol. 38, no. 4, pp. 349–362 (2016).
[5] P. Barry, “A Catalan transform and related transformations on integer sequences,” Journal of Integer Sequences, vol. 8, pp. 1–24 (2005).
[6] C. Tsang, M. N. Theorey, and W. Stein, “Fermat numbers,” University of Washington (2010). [Online]. Available: https://wstein.org/edu/2010/414/projects/tsang.pdf
[7] A. Boussayoud, M. Chelgham, and S. Boughaba, “On some identities and generating functions for Mersenne numbers and polynomials,” Turkish Journal of Analysis and Number Theory, vol. 6, no. 3, pp. 93–97 (2018).
[8] E. Eser, B. Kuloğlu, and E. Özkan, “On the Mersenne and Mersenne-Lucas hybrinomial quaternions,” Bulletin of the Transilvania University of Brașov, Series III: Mathematics and Computer Science (2023), doi: 10.31926/but.mif.2023.3.65.1.10.
[9] B. Kuloğlu, “Gaussian Fermat Numbers, Polynomials and Their Associated Transforms,” Journal of Science and Arts, vol. 24, no. 3, pp. 573–590 (2024).
[10] M. Uysal, M. Kumari, B. Kuloğlu, K. Prasad, and E. Özkan, “On the Hyperbolic k-Mersenne and k-Mersenne-Lucas Octonions,” Kragujevac Journal of Mathematics, vol. 49, no. 5, pp. 765–779 (2025).
[11] R. M. Robinson, “Mersenne and Fermat numbers,” Proceedings of the American Mathematical Society, vol. 5, no. 5, pp. 842–846 (1954).
[12] A. Cvetković, P. Rajković, and M. Ivković, “Catalan numbers, The Hankel transform and Fibonacci numbers,” Journal of Integer Sequences, vol. 5, no. 1, pp. 1–8 (2002).
[13] R. Ehrenborg, “The Hankel determinant of exponential polynomials,” The American Mathematical Monthly, vol. 107, no. 6, pp. 557–560 (2000).
[14] P. Peart and W. J. Woan, “Generating functions via Hankel and Stieltjes matrices,” Journal of Integer Sequences, vol. 3, no. 00.2, p. 1 (2000).
[15] M. Taştan and E. Özkan, “Catalan transform of the k-Jacobsthal sequence,” Electronic Journal of Mathematical Analysis and Applications, vol. 8, no. 2, pp. 70–74 (2020).
[16] N. J. A. Sloane, “The On-Line Encyclopedia of Integer Sequences,” OEIS Foundation (2023). [Online]. Available: https://oeis.org
[17] Ö. Deveci and A. Shannon, “On the complex-type Catalan transform of the k-Fibonacci numbers,” Journal of Integer Sequences, vol. 25, no. 4, pp. 1352–1367 (2022).
[18] M. Bernstein and N. J. A. Sloane, “Some canonical sequences of integers,” Linear Algebra and its Applications, vol. 226/228, pp. 57–72 (1995).
