Results 21 to 30 of about 1,912,276 (202)

Relationships Between Generalized Bernoulli Numbers and Polynomials and Generalized Euler Numbers and Polynomials [PDF]

, 2002
In this paper, concepts of the generalized Bernoulli and Euler numbers and polynomials are introduced, and some relationships between them are ...
Qi, Feng, Luo, Qiu-Ming
core   +6 more sources

Solutions of equations x2−(p2q2±3p)y2=±kt

Examples and Counterexamples, 2022
In the present paper, we have solved the equation x2−(p2q2±3p)y2=kt,x2−(p2q2±5p)y2=ktand expressed its positive integer solutions in terms of generalized Fibonacci, generalized Lucas and generalized Pell, generalized Pell–Lucas sequences.
Roji Bala, Vinod Mishra
doaj   +1 more source

Non-Fisherian generalized Fibonacci numbers [PDF]

Notes on Number Theory and Discrete Mathematics
Using biology as inspiration, this paper explores a generalization of the Fibonacci sequence that involves gender biased sexual reproduction. The female, male, and total population numbers along with their associated recurrence relations are considered ...
Thor Martinsen
doaj   +1 more source

There are no multiply-perfect Fibonacci numbers [PDF]

, 2011
Here, we show that no Fibonacci number (larger than 1) divides the sum of its ...
Lewis, Ryan H., Togbe, Alain, Kevin A. Broughan, Huguet, V. Janitzio Mejia, Marcos J. González, Broughan, Kevin A., Luca, Florian, V. Janitzio Mejía Huguet, Ryan H. Lewis, Alain Togbé, Gonzalez, Marcos J., Florian Luca   +11 more
core   +1 more source

Binomial Sum Relations Involving Fibonacci and Lucas Numbers

AppliedMath, 2023
In this paper, we provide a first systematic treatment of binomial sum relations involving (generalized) Fibonacci and Lucas numbers. The paper introduces various classes of relations involving (generalized) Fibonacci and Lucas numbers and different ...
Kunle Adegoke, Robert Frontczak, Taras Goy   +2 more
doaj   +1 more source

On a generalization of dual-generalized complex Fibonacci quaternions [PDF]

Notes on Number Theory and Discrete Mathematics, 2023
In this study, we introduce a new class of generalized quaternions whose components are dual-generalized complex Horadam numbers. We investigate some algebraic properties of them.
Elif Tan, Umut Öcal
doaj   +1 more source

On Divisibility of Generalized Fibonacci Numbers

Integers, 2015
See the abstract in the attached pdf.
Miho Aoki, Yuho Sakai
openaire   +4 more sources

Square numbers, square pyramidal numbers, and generalized Fibonacci polynomials

Journal of New Results in Science, 2022
In this paper, we derive two interesting formulas for square and square pyramidal numbers. We focus on the linear recurrence relation with constant coefficients for square and square pyramidal numbers.
Adem Şahin
doaj   +1 more source

Generalized sums of Fibonacci and Lucas Numbers [PDF]

, 2021
Here we are proposing generalized sums for Fibonacci and Lucas numbers. In the case of the Fibonacci sequence, the generalized sum contains four Fibonacci numbers.
Sparavigna, Amelia Carolina, Sparavigna, A. C.   +1 more
core   +1 more source

On Fibonacci (k,p)-Numbers and Their Interpretations

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define new kinds of Fibonacci numbers, which generalize both Fibonacci, Jacobsthal, Narayana numbers and Fibonacci p-numbers in the distance sense, using the definition of a distance between numbers by a recurrence relation according to
Berke Cengiz, Yasemin Taşyurdu
doaj   +1 more source