Results 1 to 10 of about 4,398 (223)
On (k,p)-Fibonacci Numbers [PDF]
Mathematics, 2021 In this paper, we introduce and study a new two-parameters generalization of the Fibonacci numbers, which generalizes Fibonacci numbers, Pell numbers, and Narayana numbers, simultaneously.
Natalia Bednarz
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An inequality for Fibonacci numbers [PDF]
Mathematica Bohemica, 2022 Summary: We extend an inequality for Fibonacci numbers published by \textit{P. G. Popescu} and \textit{J. L. Díaz-Barrero} in [JIPAM, J. Inequal. Pure Appl. Math. 7, No. 2, Paper No. 41, 5 p. (2006; Zbl 1132.26011)].
Horst Alzer, Florian Luca
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Some Identities Involving Fibonacci Polynomials and Fibonacci Numbers [PDF]
Mathematics, 2018 The aim of this paper is to research the structural properties of the Fibonacci polynomials and Fibonacci numbers and obtain some identities. To achieve this purpose, we first introduce a new second-order nonlinear recursive sequence. Then, we obtain our
Wenpeng Zhang
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There are No Multiply-Perfect Fibonacci Numbers [PDF]
Integers, 2011 AbstractWe show that no Fibonacci number (larger than 1) divides the sum of its divisors.
Kevin A. Broughan +5 more
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Curious Generalized Fibonacci Numbers
Mathematics, 2021 A generalization of the well-known Fibonacci sequence is the k−Fibonacci sequence whose first k terms are 0,…,0,1 and each term afterwards is the sum of the preceding k terms. In this paper, we find all k-Fibonacci numbers that are curious numbers (i.e.,
Jose L. Herrera +2 more
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On the arrowhead-Fibonacci numbers
Open Mathematics, 2016 In this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties.
Gültekin Inci, Deveci Ömür
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Some Properties of Fibonacci Numbers, Generalized Fibonacci Numbers and Generalized Fibonacci Polynomial Sequences [PDF]
Kyungpook mathematical journal, 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.
Laugier, Alexandre, Saikia, Manjil P.
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Glasnik matematički, 2016 For an integer k≥ 2, let (Fn(k))n be the k-Fibonacci sequence which starts with 0,...,0,1 (k terms) and each term afterwards is the sum of the k preceding terms. In this paper, we find all k-Fibonacci numbers which are Mersenne numbers, i.e., k-Fibonacci numbers that are equal to 1 less than a power of 2.
Bravo, Jhon J., Gómez, Carlos A.
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Abstract The Fibonacci numbers are introduced and carefully developed together with a bit of biography of Fibonacci himself. He is best known for promoting the use of Hindu-Arabic numerals in Europe and especially for his “rabbit problem” which introduces the Fibonacci numbers. Of special interest is the decimal expansion for 1/89 having
Salamone, Maya
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Altered Numbers of Fibonacci Number Squared
Journal of New Theory, 2023 We investigate two types of altered Fibonacci numbers obtained by adding or subtracting a specific value $\{a\}$ from the square of the $n^{th}$ Fibonacci numbers $G^{(2)}_{F(n)}(a)$ and $H^{(2)}_{F(n)}(a)$.
Emre Kankal, Fikri Köken
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