Results 11 to 20 of about 255,151 (329)
The GCD Sequences of the Altered Lucas Sequences [PDF]
Annales Mathematicae Silesianae, 2020 In this study, we give two sequences {L+n}n≥1 and {L−n}n≥1 derived by altering the Lucas numbers with {±1, ±3}, terms of which are called as altered Lucas numbers.
Koken Fikri
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Gessel-Lucas congruences for sporadic sequences [PDF]
Monatshefte für Mathematik, 2023 17 ...
Armin Straub
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(Verifiable) Delay Functions from Lucas Sequences [PDF]
, 2023 Lucas sequences are constant-recursive integer sequences with a long history of applications in cryptography, both in the design of cryptographic schemes and cryptanalysis. In this work, we study the sequential hardness of computing Lucas sequences over an RSA modulus. First, we show that modular Lucas sequences are at least as sequentially hard as the
Charlotte Hoffmann +3 more
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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 R. Hashim, Szabolcs Tengely
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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.
Ahmet Daşdemir
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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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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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THE SQUARE TERMS IN GENERALIZED LUCAS SEQUENCES [PDF]
Mathematika, 2013 Summary: Let \(P\) and \(Q\) be non-zero integers. The generalized Fibonacci sequence \(\{U_n\} \) and Lucas sequence \(\{V_n\}\) are defined by \(U_0 = 0\), \(U_1 = 1\) and \(U_{n+1} = PU_n + QU_{n-1}\) for \(n\geq 1\) and \(V_0 = 2\), \(V_1 = P\) and \(V_{n+1} = PV_n + QV_{n-1} \) for \(n\geq 1\), respectively.
Zafer Şi̇ar, Refık Keskin
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Supercongruences involving Lucas sequences [PDF]
Monatshefte für Mathematik, 2021 26 pages, refined ...
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Melham's sums for some Lucas polynomial sequences [PDF]
Notes on Number Theory and Discrete MathematicsA Lucas polynomial sequence is a pair of generalized polynomial sequences that satisfy the Lucas recurrence relation. Special cases include Fibonacci polynomials, Lucas polynomials, and Balancing polynomials.
Chan-Liang Chung, Chunmei Zhong
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