On Third-Order Bronze Fibonacci Numbers

Akbiyik, Mücahit; Alo, Jeta

doi:10.3390/math9202606

Cited by 10 publications

(1 citation statement)

References 11 publications

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“…Following this study, different methods in this field have been constructed. (see [4,5,12,14,15,16,19,20,25]) There have been studies on Fibonacci and related polynomials' encryption and decryption available in the literature. ( [17], [21], [22]) On the other hand, a new cryptography method based on Golden matrices is introduced in [18].…”

Section: Introductionmentioning

confidence: 99%

Coding theory for h(x)-Fibonacci polynomials

ÖZTUNÇ KAYMAK

2024

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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The amount of information transmitted over the internet network has dramatically increased with the prevailing of internet use. As a result of this increase, the algorithms used in data encryption methods have gained importance. In this paper, h(x)-Fibonacci coding/decoding method for h(x)-Fibonacci polynomials is introduced. The proposed method is fast because it is based on basic matrix operations, and it is suitable for cryptographic applications because it uses the ASCII character encoding system. For this reason, it differs from the classical algebraic methods in literature. Furthermore, the fact that h(x) is a polynomial improves the security of cryptography.

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Section: Introductionmentioning

confidence: 99%

Coding theory for h(x)-Fibonacci polynomials

ÖZTUNÇ KAYMAK

2024

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi

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Some Identities for Balancing and Lucas-Balancing Numbers in Bidimensional Version

Chimpanzo,

Catarino,

Otero-Espinar

2012

Springer Proceedings in Mathematics &Amp; Statistics

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Copper ratio obtained by generalizing the Fibonacci sequence

Özkan,

Akkuş

2024

AIP Advances

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In this study, we define a new generalization of the Fibonacci sequence that gives the copper ratio, and we will call it the copper Fibonacci sequence. In addition, inspired by the copper Fibonacci definition, we also define copper Lucas sequences, and then we give the relationships between the terms of these sequences. We present some properties, such as the Binet formulas, special summation formulas, special generating functions, etc. We find the relationships between the roots of the characteristic equation of these sequences and the general terms of these sequences. What is interesting here is that the relationships obtained from that between the roots of the characteristic equation of these new sequences and the terms of the sequences are satisfied in both roots. In addition, we examine the relationships between these sequences with the classic Fibonacci and Lucas sequences. Moreover, we calculate some identities of these sequences, such as Cassini and Catalan. Then Catalan transformation is applied to these sequences, and their terms are found. Furthermore, we apply Hankel transform to the Catalan transform of these sequences. Besides, we associate the terms of the Hankel transformation of the Catalan copper Fibonacci sequence with the classical Fibonacci numbers and the terms of the Hankel transformation of the Catalan copper Lucas sequence with the terms of the copper Lucas sequence. We present the application of copper Fibonacci and copper Lucas sequences to hyperbolic quaternions. Finally, the terms of the copper Fibonacci and copper Lucas sequences are associated with their hyperbolic quaternion values.

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On Third-Order Bronze Fibonacci Numbers

Cited by 10 publications

References 11 publications

Coding theory for h(x)-Fibonacci polynomials

Coding theory for h(x)-Fibonacci polynomials

Some Identities for Balancing and Lucas-Balancing Numbers in Bidimensional Version

Copper ratio obtained by generalizing the Fibonacci sequence

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