Results 21 to 30 of about 21,260 (290)
Decomposition of terms in Lucas sequences
Journal of Logic and Analysis, 2009 Let N be any large integer. Proceeding directly to the factorization of N is not an easy task, even unfeasible unless N belongs to a particular family of integers. Then to surmount this major difficulty we might choose to ask about the factorization of an integer in a small neighborhood of N instead of N .
Abdelmadjid Boudaoud
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Pseudorandom generators based on Lucas Sequences
Ratio Mathematica, 1993 Pseudo-random sequence generators are the heart of Stream-cipher systems. This work presents some design criteria for such generators. based on innovative methods. To this aim the Lucas Sequences, reduced modulo a prime p.
A Di Porto, W Wolfowics
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ON THE SEQUENCES RELATED TO FIBONACCI AND LUCAS NUMBERS [PDF]
Journal of the Korean Mathematical Society, 2005 The sequences \(\{U_n\}_{n\geq 0}\) and \(\{V_n\}_{n\geq 0}\) are introduced by recurrence relations: \[ \begin{aligned} U_n &= (q- 2)(U_{n-2}- U_{n-4},\;n\geq 4,\\ V_n &= (q-2) V_{n-2}- V_{n-4},\;n\geq 4\end{aligned} \] with initial conditions \(U_0= 0\), \(U_1= 1\), \(U_2= 1\), \(U_4= q- 1\), \(V_0= 2\), \(V_1= 1\), \(V_2= q-1\), where \(q\geq 5\) is
Nihal Özgur
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The relations between bi-periodic jacobsthal and bi-periodic jacobsthal lucas sequence
Cumhuriyet Science Journal, 2021 In this paper, one of the special integer sequences, Jacobsthal and Jacobsthal Lucas sequences which are encountered in computer science is generalized according to parity of the index of the entries of the sequences, called bi-periodic Jacobsthal and ...
Şükran Uygun
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Pseudoprimality related to the generalized Lucas sequences [PDF]
, 2021 Some arithmetic properties and new pseudoprimality results concerning generalized Lucas sequences are presented. The findings are connected to the classical Fibonacci, Lucas, Pell, and Pell–Lucas pseudoprimality.
Andrica, Dorin, Bagdasar, Ovidiu
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On some links between the generalised Lucas pseudoprimes of level k
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2023 Pseudoprimes are composite integers sharing behaviours of the prime numbers, often used in practical applications like public-key cryptography. Many pseudoprimality notions known in the literature are defined by recurrent sequences.
Andrica Dorin +2 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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On properties of generalized Tridovan numbers [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we examine generalized Tridovan sequences and treat in detail two cases called Tridovan sequences and Tridovan–Lucas sequences. We present Binet's formulas, generating functions, Simson formulas, and the summation formulas for these ...
Yüksel Soykan +2 more
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On Generalized Jacobsthal and Jacobsthal–Lucas Numbers
Annales Mathematicae Silesianae, 2022 Jacobsthal numbers and Jacobsthal–Lucas numbers are some of the most studied special integer sequences related to the Fibonacci numbers. In this study, we introduce one parameter generalizations of Jacobsthal numbers and Jacobsthal–Lucas numbers.
Bród Dorota, Michalski Adrian
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A Note on Two Fundamental Recursive Sequences
Annales Mathematicae Silesianae, 2021 In this note, we establish some general results for two fundamental recursive sequences that are the basis of many well-known recursive sequences, as the Fibonacci sequence, Lucas sequence, Pell sequence, Pell-Lucas sequence, etc.
Farhadian Reza, Jakimczuk Rafael
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