Results 11 to 20 of about 17,245 (264)
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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Supercongruences involving Lucas sequences [PDF]
Monatshefte für Mathematik, 2021 26 pages, refined ...
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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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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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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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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 Generalized Lucas Pseudoprimality of Level k
Mathematics, 2021 We investigate the Fibonacci pseudoprimes of level k, and we disprove a statement concerning the relationship between the sets of different levels, and also discuss a counterpart of this result for the Lucas pseudoprimes of level k.
Dorin Andrica, Ovidiu Bagdasar
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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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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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Generalized Fibonacci-Lucas Sequence [PDF]
Turkish Journal of Analysis and Number Theory, 2014 The Fibonacci sequence is a source of many nice and interesting identities. A similar interpretation exists for Lucas sequence. The Fibonacci sequence, Lucas numbers and their generalization have many interesting properties and applications to almost every field.
Bijendra Singh +2 more
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