Algebraic relations for reciprocal sums of Fibonacci numbers
Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2007)
Acta Arithmetica
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Displaying similar documents to “An inductive method for proving the transcendence of certain series”
Algebraic relations for reciprocal sums of Fibonacci numbers
A generalization of the Cassini formula
Alexey Stakhov (2012)
Visual Mathematics
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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.
Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Mohammad Farrokhi, D.G. (2009)
Integers
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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.
Algebraic independence results for reciprocal sums of Fibonacci numbers
Carsten Elsner, Shun Shimomura, Iekata Shiokawa (2011)
Acta Arithmetica
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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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The Family of Metallic Means
Vera W. de Spinadel (1999)
Visual Mathematics
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Period of a linear recurrence
A. Vince (1981)
Acta Arithmetica
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On Fibonacci-like sequences.
Vinh, Le Anh (2007)
Journal of Integer Sequences [electronic only]
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On the equation x² + dy² = Fₙ
Christian Ballot, Florian Luca (2007)
Acta Arithmetica
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Mahler's classification of numbers compared with Koksma's
Yann Bugeaud (2003)
Acta Arithmetica
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On binomial sums for the general second order linear recurrence.
Kiliç, Emrah, Tan, Elif (2010)
Integers
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Pure powers and power classes in recurrence sequences
Péter Kiss (1994)
Mathematica Slovaca
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Gelin-Cesáro identities for Fibonacci and Lucas quaternions
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.