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Coincidences in generalized Lucas sequences [PDF]
The Fibonacci Quarterly, 2014 For an integer $k\geq 2$, let $(L_{n}^{(k)})_{n}$ be the $k-$generalized Lucas sequence which starts with $0,\ldots,0,2,1$ ($k$ terms) and each term afterwards is the sum of the $k$ preceding terms.
Bravo, Eric F. +2 more
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Elliptic Solutions of Dynamical Lucas Sequences [PDF]
Entropy, 2021 We study two types of dynamical extensions of Lucas sequences and give elliptic solutions for them. The first type concerns a level-dependent (or discrete time-dependent) version involving commuting variables. We show that a nice solution for this system is given by elliptic numbers. The second type involves a non-commutative version of Lucas sequences
Schlosser, Michael J., Yoo, Meesue
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Mathematica Bohemica, 2021 Summary: Let \((G_{n})_{n\geq 1}\) be a binary linear recurrence sequence that is represented by the Lucas sequences of the first and second kind, which are \(\{U_n\}\) and \(\{V_n\}\), respectively. We show that the Diophantine equation \(G_n=B\cdot(g^{lm}-1)/(g^{l}-1)\) has only finitely many solutions in \(n,m\in\mathbb{Z}^+\), where \(g\geq 2 ...
Hayder Raheem Hashim, Szabolcs Tengely
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Oscillatory Nonautonomous Lucas Sequences [PDF]
International Journal of Differential Equations, 2009 The oscillatory behavior of the solutions of the second‐order linear nonautonomous equation x(n + 1) = a(n)x(n) − b(n)x(n − 1), n ∈ ℕ0, where a, b : ℕ0 → ℝ, is studied. Under the assumption that the sequence b(n) dominates somehow a(n), the amplitude of the oscillations and the asymptotic behavior of its solutions are also analized.
Ferreira, José M., Pinelas, Sandra
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On the intersections of Fibonacci, Pell, and Lucas numbers [PDF]
, 2010 We describe how to compute the intersection of two Lucas sequences of the forms $\{U_n(P,\pm 1) \}_{n=0}^{\infty}$ or $\{V_n(P,\pm 1) \}_{n=0}^{\infty}$ with $P\in\mathbb{Z}$ that includes sequences of Fibonacci, Pell, Lucas, and Lucas-Pell numbers.
Bilu +13 more
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Supercongruences involving Lucas sequences [PDF]
Monatshefte für Mathematik, 2021 26 pages, refined ...
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On members of Lucas sequences which are products of factorials [PDF]
, 2019 Here, we show that if $\{U_n\}_{n\ge 0}$ is a Lucas sequence, then the largest $n$ such that $|U_n|=m_1!m_2!\cdots m_k!$ with ...
Laishram, Shanta +2 more
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A method to decrease computation time for fourth order Lucas sequence [PDF]
, 2013 The fourth order Lucas sequence is a linear recurrence relation related to quartic polynomial and based on Lucas function. This sequence had been used to develop the LUC4,6 cryptosystem.
Koo, Lee Feng +3 more
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Journal of the Indonesian Mathematical Society, 2023 Horadam introduced a generalized sequence of numbers, describing its key features and the special sub-sequences obtained from specific choices of initial parameters. This sequence and its sub-sequences are known as the Horadam, generalized Fibonacci, and generalized Lucas numbers, respectively.
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Balancing and Lucas-Balancing Numbers and their Application to Cryptography [PDF]
, 2016 It is well known that, a recursive relation for the sequence  is an equation that relates  to certain of its preceding terms .
Kumar Ray, Prasanta +2 more
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