Results 1 to 10 of about 25,534 (310)
Gessel-Lucas congruences for sporadic sequences [PDF]
Monatshefte für Mathematik, 2023 17 ...
Armin Straub
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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. In this paper, we find all the integers that appear in different generalized Lucas sequences; i.e., we study the Diophantine equation $L_n^{(k)}=L_m^{(\ell)
Eric F. Bravo +2 more
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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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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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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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Shifted powers in Lucas–Lehmer sequences [PDF]
Research in Number Theory, 2019 We develop a general framework for finding all perfect powers in sequences derived by shifting non-degenerate quadratic Lucas-Lehmer binary recurrence sequences by a fixed integer. By combining this setup with bounds for linear forms in logarithms and results based upon the modularity of elliptic curves defined over totally real fields, we are able to ...
Michael A. Bennett +2 more
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Blocks within the period of Lucas sequence
Ratio Mathematica, 2021 In this paper, we consider the periodic nature of the sequence of Lucas numbers L_n defined by the recurrence relation L_n= L_(n-1)+L_(n-2); for all n≥2; with initial condition L_0=2 and L_1=1.
Rima P. Patel, Dr. Devbhadra V. Shah
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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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Encryption and Decryption of the Data by Using the Terms of the Lucas Series
Düzce Üniversitesi Bilim ve Teknoloji Dergisi, 2021 The sequence, whose initial condition is 2 and 1, obtained by summing the two terms preceding it, is called the Lucas sequence. The terms of this series continue as 2, 1, 3, 4, 7, 11, 18, 29, ... respectively. The features of the Lucas sequence have been
Mehmet Duman, Merve Güney Duman
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