Geodesic
On generalized Mersenne hybrid numbers
Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 74 (2020) no. 1

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The hybrid numbers are generalization of complex, hyperbolic and dual numbers. In this paper we consider  a special kind of hybrid numbers, namely the Mersenne hybrid numbers and we give some of their properties.
Keywords: Mersenne numbers, recurrence relations, complex numbers, hyperbolic numbers, dual numbers 
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Szynal-Liana, Anetta; Włoch, Iwona. On generalized Mersenne hybrid numbers. Annales Universitatis Mariae Curie-Skłodowska. Mathematica, Tome 74 (2020) no. 1. http://geodesic.mathdoc.fr/item/AUM_2020_74_1_a2/

[1] Bednarz, U., Włoch, I., Wołowiec-Musiał, M., Total graph interpretation of the numbers of the Fibonacci type, J. Appl. Math. (2015), Article ID 837917, 7 pp., http://dx.doi.org/10.1155/2015/837917.

[2] Horadam, A. F., Basic properties of a certain generalized sequence of numbers, Fibonacci Quart. 3 (3) (1965), 161–176.

[3] Ochalik, P., Włoch, A., On generalized Mersenne numbers, their interpretations and matrix generators, Ann. Univ. Mariae Curie-Skłodowska Sect. A 72 (1) (2018), 69–76, http://dx.doi.org/10.17951/a.2018.72.1.69-76.

[4] Ozdemir, M., Introduction to hybrid numbers, Adv. Appl. Clifford Algebr. 28 (2018), Article ID 11, https://doi.org/10.1007/s00006-018-0833-3.

[5] Szynal-Liana, A., The Horadam hybrid numbers, Discuss. Math. Gen. Algebra Appl. 38 (1) (2018), 91–98, http://dx.doi.org/10.7151/dmgaa.

[6] Szynal-Liana, A., Włoch, I., On Jacobsthal and Jacobsthal–Lucas hybrid numbers, Ann. Math. Sil. (2018), https://doi.org/10.2478/amsil-2018-0009.

[7] Szynal-Liana, A., Włoch, I., On Pell and Pell–Lucas hybrid numbers, Comment. Math. 58 (1–2) (2018), 11–17, https://doi.org/10.14708/cm.v58i1-2.6364.

[8] Szynal-Liana, A., Włoch, I., The Fibonacci hybrid numbers, Util. Math. 110 (2019), 3–10.