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

Voir la notice de l'article provenant de la source Library of Science

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
@article{AUM_2020_74_1_a2,
     author = {Szynal-Liana, Anetta and W{\l}och, Iwona},
     title = {On generalized {Mersenne} hybrid numbers},
     journal = {Annales Universitatis Mariae Curie-Sk{\l}odowska. Mathematica },
     publisher = {mathdoc},
     volume = {74},
     number = {1},
     year = {2020},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/AUM_2020_74_1_a2/}
}
TY  - JOUR
AU  - Szynal-Liana, Anetta
AU  - Włoch, Iwona
TI  - On generalized Mersenne hybrid numbers
JO  - Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
PY  - 2020
VL  - 74
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/AUM_2020_74_1_a2/
LA  - en
ID  - AUM_2020_74_1_a2
ER  - 
%0 Journal Article
%A Szynal-Liana, Anetta
%A Włoch, Iwona
%T On generalized Mersenne hybrid numbers
%J Annales Universitatis Mariae Curie-Skłodowska. Mathematica 
%D 2020
%V 74
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/AUM_2020_74_1_a2/
%G en
%F AUM_2020_74_1_a2
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.