Generalization of a result of Hoggatt and Bergum on Fibonacci numbers
Morgado, José (1983-1984)
Portugaliae mathematica
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Displaying similar documents to “Fibonacci numbers and Diophantine quadruples: generalizations of results of Morgado and Horadam”
Generalization of a result of Hoggatt and Bergum on Fibonacci numbers
On the resolution of simultaneous Pell equations.
Szalay, László (2007)
Annales Mathematicae et Informaticae
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Note on some results of A.F. Horadam and A.G. Shannon concerning a Catalan's identity on Fibonacci numbers
Morgado, José (1987)
Portugaliae mathematica
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Some remarks on an identity of Catalan concerning the Fibonacci numbers
Morgado, José (1980)
Portugaliae mathematica
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Two equations for linear recurrence sequences
V. Losert (2005)
Acta Arithmetica
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A generalization of the Cassini formula
Alexey Stakhov (2012)
Visual Mathematics
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Generalization of identities of Catalan and others
Horadam, A.F., Shannon, A.G. (1987)
Portugaliae mathematica
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Generalization of an identity involving the generalized Fibonacci numbers and its applications.
Mohammad Farrokhi, D.G. (2009)
Integers
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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.
Diophantine equations with products of consecutive terms in Lucas sequences II
Florian Luca, T. N. Shorey (2008)
Acta Arithmetica
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Generalization of a result of Morgado
Horadam, A.F. (1987)
Portugaliae mathematica
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Perfect powers in linear recurring sequences
Clemens Fuchs, Robert F. Tichy (2003)
Acta Arithmetica
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Pell’s Equation
Marcin Acewicz, Karol Pąk (2017)
Formalized Mathematics
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In this article we formalize several basic theorems that correspond to Pell’s equation. We focus on two aspects: that the Pell’s equation x2 − Dy2 = 1 has infinitely many solutions in positive integers for a given D not being a perfect square, and that based on the least fundamental solution of the equation when we can simply calculate algebraically each remaining solution. “Solutions to Pell’s Equation” are listed as item #39 from the “Formalizing 100 Theorems” list maintained by Freek...
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.