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Fibonacci numbers which are concatenation of three Fibonacci or Lucas numbers
Punjab University Journal of MathematicsIn this note, we show that there is no Fibonacci number that can be expressed as a concatenation of three Fibonacci or Lucas numbers under a certain constraint. That is, we solve to the Diophantine equations Fn = 10d+lFm1 + 10lFm2 + Fm3 and Fn = 10d+lLm1 + 10lLm2 + Lm3 in non-negative integers (n, m1, m2, m3) with m2 ≤ m1, where d and l represent the ...
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Simple integral representations for the Fibonacci and Lucas numbers
2022Summary: Integral representations of the Fibonacci numbers \(F_{kn+r}\) and the Lucas numbers \(L_{kn+r}\) are presented. Each is established using methods that rely on nothing beyond elementary integral calculus.
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k-Fibonacci and k-Lucas Numbers as Product of Two Repdigits
Results in Mathematics, 2021Salah Eddine Rihane, Rihane Salah Eddine
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On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications
Communications in Algebra, 2020Engin Özkan, Merve Tastan
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Multiplicative dependence between k-Fibonacci and k-Lucas numbers
Periodica Mathematica Hungarica, 2020CARLOS A Gomez +2 more
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Incomplete Fibonacci and Lucasp-numbers
Mathematical and Computer Modelling, 2010Dursun Taşci̧
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Some identities for the generalized Fibonacci numbers and the generalized Lucas numbers
Applied Mathematics and Computation, 2013Andrzej Włoch
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Some identities of the generalized Fibonacci and Lucas sequences
Applied Mathematics and Computation, 2018Zhizheng Zhang
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