Results 21 to 30 of about 1,163,753 (215)
Carlitz's Equations on Generalized Fibonacci Numbers
Symmetry, 2022 Carlitz solved some Diophantine equations on Fibonacci or Lucas numbers. We extend his results to the sequence of generalized Fibonacci and Lucas numbers.
Min Wang, Peng Yang, Yining Yang
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“Generating matrix for Generalized Fibonacci numbers and Fibonacci polynomials
Journal of Physics: Conference Series, 2022 Many researchers have been working on recurrence relation sequences of numbers and polynomials which are useful topic not only in mathematics but also in physics, economics and various applications in many other fields.
Mannu Arya, V. Verma
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On the sum of the reciprocals of k-generalized Fibonacci numbers
Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2022 In this note, we that if { Fn(k) }n≥0 {\left\{ {F_n^{\left( k \right)}} \right\}_{n \ge 0}} denotes the k-generalized Fibonacci sequence then for n ≥ 2 the closest integer to the reciprocal of ∑m≥n1/Fm(k) \sum\nolimits_{m \ge n} {1/F_m^{\left( k \right)}}
Adel Alahmadi, F. Luca
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Some properties of k-generalized Fibonacci numbers
, 2021 Fn (k) = (Fm) (Fm+1) r , n = mk + r. In [14], Özkan et al. defined a new family of k-Lucas numbers and gave some identities of the new family of k-Fibonacci and k-Lucas numbers. Özkan et al.
N. Yilmaz, A. Aydoğdu, E. Özkan
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Archives of Current Research International, 2021 In this paper, closed forms of the summation formulas ∑nk=0 xkWmk+j for generalized Fibonacci numbers are presented. As special cases, we give summation formulas of Fibonacci, Lucas, Pell, Pell-Lucas, Jacobsthal, Jacobsthal-Lucas numbers.
Y. Soykan
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On the problem of Pillai with k-generalized Fibonacci numbers and powers of 3 [PDF]
International Journal of Number Theory, 2020 For an integer [Formula: see text], let [Formula: see text] be the [Formula: see text]-generalized Fibonacci sequence which starts with [Formula: see text] (a total of [Formula: see text] terms) and for which each term afterwards is the sum of the ...
Mahadi Ddamulira, Florian Luca
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On some 3 × 3 dimensional matrices associated with generalized Fibonacci numbers
Notes on Number Theory and Discrete Mathematics, 2021 In this work, it is presented a procedure to find some 3 × 3 dimensional matrices whose integer powers can be characterized by generalized Fibonacci numbers. Moreover, some numerical examples are given to exemplify the procedure established.
H. Özdemir, Sinan Karakaya, T. Petik
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GCD of Sums of k Consecutive Squares of Generalized Fibonacci Numbers
The Fibonacci quarterly, 2022 In 2021, Guyer and Mbirika gave two equivalent formulas that computed the greatest common divisor (GCD) of all sums of k consecutive terms in the generalized Fibonacci sequence ( G n ) n ≥ 0 given by the recurrence G n = G n − 1 + G n − 2 for all n ≥ 2 ...
A. Mbirika, Jurgen Spilker
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Quantum coin flipping, qubit measurement, and generalized Fibonacci numbers [PDF]
Theoretical and mathematical physics, 2021 The problem of Hadamard quantum coin measurement in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength ...
O. Pashaev
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Simson Identity of Generalized m-step Fibonacci Numbers [PDF]
International Journal of Advances in Applied Mathematics and Mechanics, 2019 One of the best known and oldest identities for the Fibonacci sequence $F_n$ is $F_{n+1}F_{n-1}-F_{n}^2=(-1)^n$ which was derived first by R. Simson in 1753 and it is now called as Simson or Cassini Identity. In this paper, we generalize this result to generalized m-step Fibonacci numbers and give an attractive formula.
Yüksel Soykan
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