• Kyungpook Mathematical Journal
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• v.57 no.1
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• pp.1-84
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• 2017

In this paper we study the Fibonacci numbers and derive some interesting properties and recurrence relations. We prove some charecterizations for $F_p$, where p is a prime of a certain type. We also define period of a Fibonacci sequence modulo an integer, m and derive certain interesting properties related to them. Afterwards, we derive some new properties of a class of generalized Fibonacci numbers. In the last part of the paper we introduce some generalized Fibonacci polynomial sequences and we derive some results related to them.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.201-210
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• 2024

In this paper, we construcr the q-Bernoulli-Fibonacci numbers and polynomials. Finally, we investigate the distribution of the zeros of the q-Bernoulli-Fibonacci polynomials by using computer.

• Honam Mathematical Journal
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• v.40 no.1
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• pp.199-210
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• 2018

In this paper we obtain some formulae for several sums of generalized Fibonacci numbers $U_n$ and generalized Lucas numbers $V_n$ and their dual forms $G_n$ and $H_n$ by using extensions of an interesting identity by A. R. Amini for Fibonacci numbers to these four kinds of generalizations and their first and second derivatives.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.535-547
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• 2019

In this paper, by using the lower bound of linear forms in logarithms of Matveev and the theory of continued fractions by means of a variation of a result of Dujella and $Peth{\ddot{o}}$, we find all generalized Fibonacci numbers which are Pell numbers. This paper continues a previous work that searched for Pell numbers in the Fibonacci sequence.

• Journal of Applied and Pure Mathematics
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• v.6 no.1_2
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• pp.47-54
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• 2024

In this paper, we investigate the distribution of the zeros of the Bernoulli-Fibonacci polynomials by using computer.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.473-484
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• 2022

In this study, some new relations between generalized Fibonacci numbers and matrices are given. The work is designed in three stages: Firstly, it is obtained a relation between generalized Fibonacci numbers and integer powers of the matrices X satisfying the relation X² = pX +qI, and also, many results are derived from obtained relation. Then, it is established more general relation between generalized Fibonacci numbers and the square matrices X satisfying the condition X² = V_nX - (-q)ⁿI. Finally, some applications and numerical examples related to the obtained results are given.

• Journal of Applied and Pure Mathematics
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• v.6 no.3_4
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• pp.119-126
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• 2024

In this paper, we investigate the distribution of the zeros of the Euler-Fibonacci polynomials by using computer.

• Communications of the Korean Mathematical Society
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• v.29 no.3
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• pp.387-399
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• 2014

The ratios of any two Fibonacci numbers are expressed by means of semisimple continued fraction.

• Honam Mathematical Journal
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• v.42 no.1
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• pp.49-62
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• 2020

In this paper, we consider interesting binomial and alternating binomial triple sums evaluated in multiplication forms in terms of the Fibonacci and Lucas numbers.

• Communications of the Korean Mathematical Society
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• v.38 no.1
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• pp.89-96
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• 2023

Edgar obtained an identity between Fibonacci and Lucas numbers which generalizes previous identities of Benjamin-Quinn and Marques. Recently, Dafnis provided an identity similar to Edgar's. In the present article we give some generalizations of Edgar's and Dafnis's identities.