Results 31 to 40 of about 616 (205)
On the k-Fibonacci and k-Lucas spinors [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 In this paper, we introduce a new family of sequences called the k-Fibonacci and k-Lucas spinors. Starting with the Binet formulas we present their basic properties, such as Cassini’s identity, Catalan’s identity, d’Ocagne's identity, Vajda's identity ...
Munesh Kumari +2 more
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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 new arithmetic properties of the generalized Lucas sequences [PDF]
, 2021 Some arithmetic properties of the generalized Lucas sequences are studied, extending a number of recent results obtained for Fibonacci, Lucas, Pell, and Pell–Lucas sequences.
Andrica, Dorin, Bagdasar, Ovidiu
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Fibonacci–Lucas–Pell–Jacobsthal relations [PDF]
, 2022 In this paper, we prove several identities involving linear combinations of convolutions of the generalized Fibonacci and Lucas sequences. Our results apply more generally to broader classes of second-order linearly recurrent sequences with constant ...
Goy, Taras +2 more
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Solutions of equations x2−(p2q2±3p)y2=±kt
Examples and Counterexamples, 2022 In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
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Identities relating six members of the Fibonacci family of sequences
Karpatsʹkì Matematičnì Publìkacìï, 2022 In this paper, we prove several identities each relating a sum of products of three terms coming from different members of the Fibonacci family of sequences with a comparable sum whose terms come from three other sequences.
R. Frontczak, T. Goy, M. Shattuck
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A note on generating primitive Pythagorean triples using matrices [PDF]
Notes on Number Theory and Discrete Mathematics, 2023 We present matrices that generate families of primitive Pythagorean triples that arise from generalized Fibonacci sequences. We then present similar results for generalized Lucas sequences and primitive Pythagorean triples.
Jathan Austin
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Generalized Fibonacci – Like Sequence Associated with Fibonacci and Lucas Sequences [PDF]
Turkish Journal of Analysis and Number Theory, 2016 The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field. Fibonacci sequence is defined by the recurrence formula Fn=Fn-1+Fn-2, , and F0=0, F1=1, where Fn is a nth number of sequence.
Yogesh Kumar Gupta +2 more
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Diophantine equations involving the bi-periodic Fibonacci and Lucas sequences [PDF]
, 2022 In this paper, we present new identities involving the biperiodic Fibonacci and Lucas sequences. Then we solve completely some quadratic Diophantine equations involving the bi-periodic Fibonacci and Lucas ...
DJOUMAKH, Akila +2 more
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On Third-Order Bronze Fibonacci Numbers
Mathematics, 2021 In this study, we firstly obtain De Moivre-type identities for the second-order Bronze Fibonacci sequences. Next, we construct and define the third-order Bronze Fibonacci, third-order Bronze Lucas and modified third-order Bronze Fibonacci sequences. Then,
Mücahit Akbiyik, Jeta Alo
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