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.
Displaying similar documents to “Gelin-Cesáro identities for Fibonacci and Lucas quaternions”
An inequality for Fibonacci numbers
Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Mohammad Farrokhi, D.G. (2009)
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Summation identities for representation of certain real numbers.
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On Balancing and Lucas-balancing Quaternions
Bijan Kumar Patel, Prasanta Kumar Ray (2021)
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The aim of this article is to investigate two new classes of quaternions, namely, balancing and Lucas-balancing quaternions that are based on balancing and Lucas-balancing numbers, respectively. Further, some identities including Binet's formulas, summation formulas, Catalan's identity, etc. concerning these quaternions are also established.
On binomial sums for the general second order linear recurrence.
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A generalization of the Cassini formula
Alexey Stakhov (2012)
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Binomials transformation formulae for scaled Fibonacci numbers
Edyta Hetmaniok, Bożena Piątek, Roman Wituła (2017)
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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
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Vera W. de Spinadel (1999)
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A WZ proof of a “curious” identity.
Ekhad, Shalosh B., Mohammed, Mohamud (2003)
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On finite summation, recurrence relations and identities of H-functions
P. Anandani (1969)
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On certain combinatorial identities
Robert Bartoszyński (1974)
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On the equation x² + dy² = Fₙ
Christian Ballot, Florian Luca (2007)
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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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