A generalization of the Cassini formula
Alexey Stakhov (2012)
Visual Mathematics
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Alexey Stakhov (2012)
Visual Mathematics
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Ahmet Daşdemir (2019)
Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica
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To date, many identities of different quaternions, including the Fibonacci and Lucas quaternions, have been investigated. In this study, we present Gelin-Cesáro identities for Fibonacci and Lucas quaternions. The identities are a worthy addition to the literature. Moreover, we give Catalan's identity for the Lucas quaternions.
Mohammad Farrokhi, D.G. (2009)
Integers
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Kiliç, Emrah, Tan, Elif (2010)
Integers
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Vera W. de Spinadel (1999)
Visual Mathematics
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Filipczak, Tomasz (2015-12-07T12:09:00Z)
Acta Universitatis Lodziensis. Folia Mathematica
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Zhang, Tianping, Ma, Yuankui (2005)
Journal of Integer Sequences [electronic only]
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Ekhad, Shalosh B., Mohammed, Mohamud (2003)
Integers
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Czesław Stępniak (2014)
Discussiones Mathematicae Probability and Statistics
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Recent model of lifetime after a heart attack involves some integer coefficients. Our goal is to get these coefficients in simple way and transparent form. To this aim we construct a schema according to a rule which combines the ideas used in the Pascal triangle and the generalized Fibonacci and Lucas numbers
Pinthira Tangsupphathawat, Narong Punnim, Vichian Laohakosol (2012)
Colloquium Mathematicae
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The problem whether each element of a sequence satisfying a fourth order linear recurrence with integer coefficients is nonnegative, referred to as the Positivity Problem for fourth order linear recurrence sequence, is shown to be decidable.
Grossman, George, Tefera, Akalu, Zeleke, Aklilu (2006)
International Journal of Mathematics and Mathematical Sciences
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Diego Marques, Alain Togbé (2011)
Colloquium Mathematicae
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In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.
Horadam, A.F., Shannon, A.G. (1987)
Portugaliae mathematica
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Kılıç, Emrah, Ulutaş, Yücel Türker, Ömür, Neşe (2011)
Journal of Integer Sequences [electronic only]
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Christian Ballot, Florian Luca (2007)
Acta Arithmetica
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Ercan Altınışık, N. Feyza Yalçın, Şerife Büyükköse (2015)
Special Matrices
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Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers. Furthermore, we show that ℱn is invertible and obtain the entries of the inverse of ℱn in terms of complex Fibonacci numbers.
Florian Luca (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2007)
Acta Arithmetica
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