Results 11 to 20 of about 187 (159)
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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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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The GCD Sequences of the Altered Lucas Sequences
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 m-extension of Fibonacci and Lucas p-difference sequences [PDF]
Filomat, 2019 In this paper we define the m-extension of Fibonacci and Lucas p-difference sequences by using the m-extension of Fibonacci and Lucas p-numbers. We investigate some properties of our new sequences and introduce some relations between the m-extension of Fibonacci and Lucas p-difference sequences and the m-extension of Fibonacci and Lucas p ...
Köme, Cahit, Yazlık, Yasin
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On Recursive Hyperbolic Fibonacci Quaternions
Communications in Advanced Mathematical Sciences, 2021 Many quaternions with the coefficients selected from special integer sequences such as Fibonacci and Lucas sequences have been investigated by a great number of researchers.
Ahmet Daşdemir
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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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Diophantine equations with Lucas and Fibonacci number coefficients [PDF]
Notes on Number Theory and Discrete MathematicsFibonacci and Lucas numbers are special number sequences that have been the subject of many studies throughout history due to the relations they provide.
Cemil Karaçam +3 more
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Generalized Fibonacci and Lucas Sequences and Rootfinding Methods [PDF]
Mathematics of Computation, 1993 Consider the sequences{un}\{ {u_n}\}and{vn}\{ {v_n}\}generated byun+1=pun−qun−1{u_{n + 1}} = p{u_n} - q{u_{n - 1}}andvn+1=pvn−qvn−1,n≥1{v_{n + 1}} = p{v_n} - q{v_{n - 1}},n \geq 1, whereu0=0,u1=1,v0=2,v1=p{u_0} = 0,{u_1} = 1,{v_0} = 2,{v_1} = p, withpandqreal and nonzero.
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New summation identities of hyperbolic k-Fibonacci and k-Lucas quaternions [PDF]
Notes on Number Theory and Discrete MathematicsIn this paper, we introduce a set of identities involving hyperbolic k-Fibonacci quaternions and k-Lucas quaternions. Moreover, we derive summation identities for hyperbolic k-Fibonacci and k-Lucas quaternions by utilizing established properties of k ...
A. D. Godase
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