Incomplete Fibonacci and Lucas <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>p</mml:mi></mml:math>-numbers

Tasci, Dursun; Firengiz, Mirac Cetin

doi:10.1016/j.mcm.2010.07.003

Cited by 33 publications

(3 citation statements)

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“…The theoretical properties of numbers obtained from homogeneous linear repetition relations relevant to our research context have been extensively studied by various authors, see, for example, refs. [12][13][14][15][16][17][18][19][20][21][22]. Their work has shed light on key aspects of this topic and provided valuable insights into the properties of Fibonacci-type sequences on elliptic curves.…”

Section: Introductionmentioning

confidence: 98%

Generalized Fibonacci Sequences for Elliptic Curve Cryptography

Cheddour,

Chillali,

Mouhib

2023

Mathematics

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The Fibonacci sequence is a well-known sequence of numbers with numerous applications in mathematics, computer science, and other fields. In recent years, there has been growing interest in studying Fibonacci-like sequences on elliptic curves. These sequences have a number of exciting properties and can be used to build new encryption systems. This paper presents a further generalization of the Fibonacci sequence defined on elliptic curves. We also describe an encryption system using this sequence which is based on the discrete logarithm problem on elliptic curves.

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Section: Introductionmentioning

confidence: 98%

Generalized Fibonacci Sequences for Elliptic Curve Cryptography

Cheddour,

Chillali,

Mouhib

2023

Mathematics

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“…For any given integer and , the Fibonacci -sequence, and the Lucas -sequence are defined recursively by and with initial conditions and for , respectively, [3][4][5][6][7][8]. Very recently, for any given integer and , the Leonardo -sequence is defined recursively by the following non-homogeneous relation (1.1) with initial conditions for , [9].…”

Section: Introduction and Fundamentalsmentioning

confidence: 99%

ON 3-PARAMETER GENERALIZED QUATERNIONS WITH THE LEONARDO p-SEQUENCE

SAÇLI

2024

J. Sci. Arts

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In this article, 3-parameter generalized quaternionic Leonardo p-sequence which is a quaternion generalization of the Leonardo p-sequence is presented. Several properties are examined by means of their homogeneous and non-homogeneous recursive relations. According to the special cases of 3-parameter λ_(i ∈ \{1,2,3\}) and p, all the results given in paper are reducible to all quaternions mentioned in this paper.

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“…n 2˘/ D L n : The generating functions of these numbers were studied by Pintér and Srivastava [17]. Many other authors have also studied this topic (see, for example, [8][9][10][11][12]18,19,21,22]).…”

Section: Introductionmentioning

confidence: 99%

Some results on the q-analogues of the incomplete Fibonacci and Lucas Polynomials

Srivástava¹,

Tuglu²,

Çetin³

2019

MMN

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In the present paper, we introduce new families of the q-Fibonacci and q-Lucas polynomials, which are represented here as the incomplete q-Fibonacci polynomials F k n .x; s; q/ and the incomplete q-Lucas polynomials L k n .x; s; q/, respectively. These polynomials provide the q-analogues of the incomplete Fibonacci and Lucas numbers. We give several properties and generating functions of each of these families q-polynomials. We also point out the fact that the results for the q-analogues which we consider in this article for 0 < q < 1 can easily be translated into the corresponding results for the .p; q/-analogues (with 0 < q < p 5 1) by applying some obvious parametric variations, the additional parameter p being redundant.

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Incomplete Fibonacci and Lucas p-numbers

Cited by 33 publications

References 5 publications

Generalized Fibonacci Sequences for Elliptic Curve Cryptography

Generalized Fibonacci Sequences for Elliptic Curve Cryptography

ON 3-PARAMETER GENERALIZED QUATERNIONS WITH THE LEONARDO p-SEQUENCE

Some results on the q-analogues of the incomplete Fibonacci and Lucas Polynomials

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