Results 241 to 250 of about 13,753 (265)

Fibonacci Numbers that Are $$\eta$$-concatenations of Leonardo and Lucas Numbers

Proceedings of the Bulgarian Academy of Sciences
Let $$\{F_{r}\}_{r\geq0}$$, $$\{L_{r}\}_{r\geq0}$$ and $$\{Le_{r}\}_{r\geq0}$$ be $$r$$-th terms of Fibonacci, Lucas and Leonardo sequences, respectively. In this paper, we determined the effective bounds for the solutions of the Diophantine equation $$F_{r}=\eta^{k}Le_{s}+L_{t}$$ in non-negative integers $$r$$, $$s$$, $$t$$, where $$k$$ represents the
Taher, Hunar Sherzad, Dash, Saroj Kumar
openaire   +2 more sources

Gaussian Quaternion Involving Leonardo Numbers

Sarajevo Journal of Mathematics
In this study, using the Leonardo numbers, we define a new type of quaternion that is called a Leonard Gaussian quaternion. We also give a negative-Leonardo Gaussian quaternion. These numbers are introduced from the set of complex numbers and quaternions. Moreover, we obtain the Binet’s formula, generating function formula, d’Ocagne’s identity, Catalan’
openaire   +2 more sources

q-Leonardo Bicomplex Numbers

2023
Abstract: In the paper, we define the $q$-Leonardo bicomplex numbers by using the $q$-integers. Also, we give some algebraic properties of $q$-Leonardo bicomplex numbers such as recurrence relation, generating function, Binet's formula, D'Ocagne's identity, Cassini's identity, Catalan's identity and Honsberger identity.
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Some Properties of Leonardo Numbers

2020
In this paper, we consider the Leonardo numbers which is defined by Catarino and Borges. Using Binet's formula of this sequence, we obtain new identities of the Leonardo numbers. Also , we give relations among the Fibonacci, Lucas and Leonardo numbers.
ALP, Yasemin, KOÇER, E. Gökçen
openaire   +1 more source

Leonardo da Vinci and Fluid Mechanics

Annual Review of Fluid Mechanics, 2021
Ivan Marusic, Susan Broomhall
exaly  

Generalized Fibonacci–Leonardo numbers

Journal of Difference Equations and Applications, 2023
Urszula Bednarz, Małgorzata Wołowiec-Musiał   +1 more
openaire   +1 more source

Leonardo da Vinci on Wear

Biotribology, 2021
W Gregory Sawyer
exaly  

On Leonardo sedenions

Afrika Matematika, 2023
Hayrullah Özimamoğlu
exaly  

On Leonardo and a fossil whale: a reappraisal with implications for the early history of palaeontology

Historical Biology, 2021
Alberto Collareta, Annalisa Berta, Giovanni Bianucci   +2 more
exaly  

Leonardo da Vinci׳s studies of friction

Wear, 2016
Ian M Hutchings
exaly