Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Mohammad Farrokhi, D.G. (2009)
Integers
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Displaying similar documents to “Gelin-Cesáro identities for Fibonacci and Lucas quaternions”
Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Summation identities for representation of certain real numbers.
Grossman, George, Tefera, Akalu, Zeleke, Aklilu (2006)
International Journal of Mathematics and Mathematical Sciences
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On binomial sums for the general second order linear recurrence.
Kiliç, Emrah, Tan, Elif (2010)
Integers
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A generalization of the Cassini formula
Alexey Stakhov (2012)
Visual Mathematics
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Binomials transformation formulae for scaled Fibonacci numbers
Edyta Hetmaniok, Bożena Piątek, Roman Wituła (2017)
Open Mathematics
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The aim of the paper is to present the binomial transformation formulae of Fibonacci numbers scaled by complex multipliers. Many of these new and nontrivial relations follow from the fundamental properties of the so-called delta-Fibonacci numbers defined by Wituła and Słota. The paper contains some original relations connecting the values of delta-Fibonacci numbers with the respective values of Chebyshev polynomials of the first and second kind.
Generalization of identities of Catalan and others
Horadam, A.F., Shannon, A.G. (1987)
Portugaliae mathematica
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The Family of Metallic Means
Vera W. de Spinadel (1999)
Visual Mathematics
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A WZ proof of a “curious” identity.
Ekhad, Shalosh B., Mohammed, Mohamud (2003)
Integers
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On finite summation, recurrence relations and identities of H-functions
P. Anandani (1969)
Annales Polonici Mathematici
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On certain combinatorial identities
Robert Bartoszyński (1974)
Colloquium Mathematicae
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On the equation x² + dy² = Fₙ
Christian Ballot, Florian Luca (2007)
Acta Arithmetica
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Fibonacci Numbers with the Lehmer Property
Florian Luca (2007)
Bulletin of the Polish Academy of Sciences. Mathematics
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We show that if m > 1 is a Fibonacci number such that ϕ(m) | m-1, where ϕ is the Euler function, then m is prime
Erratum to the Paper "Fibonacci Numbers with the Lehmer Property" (Bull. Polish Acad. Sci. Math. 55 (2007), 7-15)
Florian Luca (2011)
Bulletin of the Polish Academy of Sciences. Mathematics
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Determinants and inverses of circulant matrices with complex Fibonacci numbers
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.
Algebraic relations for reciprocal sums of Fibonacci numbers
Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2007)
Acta Arithmetica
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Some remarks on an identity of Catalan concerning the Fibonacci numbers
Morgado, José (1980)
Portugaliae mathematica
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On terms of linear recurrence sequences with only one distinct block of digits
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.