Displaying similar documents to “Bihyperbolic numbers of the Fibonacci type and their idempotent representation”

An Exercise on Fibonacci Representations

Jean Berstel (2010)

RAIRO - Theoretical Informatics and Applications

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We give a partial answer to a question of Carlitz asking for a closed formula for the number of distinct representations of an integer in the Fibonacci base.

On generalized bihyperbolic Mersenne numbers

Dorota Bród, Anetta Szynal-Liana (2024)

Mathematica Bohemica

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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.

An inequality for Fibonacci numbers

Horst Alzer, Florian Luca (2022)

Mathematica Bohemica

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We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.