Geodesic
On generalized bihyperbolic Mersenne numbers
Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 75-85
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In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.
In this paper, a new generalization of Mersenne bihyperbolic numbers is introduced. Some of the properties of presented numbers are given. A general bilinear index-reduction formula for the generalized bihyperbolic Mersenne numbers is obtained. This result implies the Catalan, Cassini, Vajda, d'Ocagne and Halton identities. Moreover, generating function and matrix generators for these numbers are presented.
DOI : 10.21136/MB.2023.0085-22
Classification : 11B37, 11B39
Keywords: Mersenne number; hyperbolic number; bihyperbolic number; recurrence relation 
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Bród, Dorota; Szynal-Liana, Anetta. On generalized bihyperbolic Mersenne numbers. Mathematica Bohemica, Tome 149 (2024) no. 1, pp. 75-85. doi: 10.21136/MB.2023.0085-22

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