Results 171 to 180 of about 1,467 (207)

INTRA RATIOS OF FIBONACCI AND LUCAS NUMBERS

JP Journal of Algebra, Number Theory and Applications, 2015
Summary: We study the ratios of any \(k\) spacing apart Fibonacci numbers and Lucas numbers as well as intra ratios \(L_n/F_{n\pm k}\) by means of semisimple continued fraction. And the semisimple continued fractions will be applied to solve certain systems of linear equation.
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Incomplete Fibonacci and Lucas numbers

Rendiconti del Circolo Matematico di Palermo, 1996
It is well known that the Fibonacci numbers \(F_n\) and the Lucas numbers \(L_n\) can be written as \[ \begin{aligned} F_n &= \sum^k_{i=0} {{n-1-i} \choose i}, \qquad \lfloor (n- 1)/2 \rfloor\leq k\leq n-1, \tag{1}\\ L_n &= \sum^k_{i=0} {n\over {n-i}} {{n-i} \choose i}, \qquad \lfloor n/2 \rfloor \leq k\leq n-1.
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Fibonacci and Lucas numbers which are product of two Jacobsal-Lucas numbers

2023
In this study, we find all Fibonacci numbers F-k and Lucas numbers L-k which are products of two Jacobsthal-Lucas numbers. More generally, taking k, m, n as nonnegative integers, we proved that F-k = j(m)j(n) = (2(m) + ((-1)(m)) . (2(n) + ((-1)(n)) implies that (k, m, n) = (1, 1, 1); (2, 1, 1), (3, 0, 1), (5, 1, 2), (9, 0, 4) and L-k = j(m)j(n) implies
Erduvan, F, Keskin, R
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Identities for Products of Fibonacci and Lucas Numbers

The Fibonacci Quarterly, 1967
Daykin, D. E., Dresel, L. A. G.
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Fibonacci numbers which are concatenation of three Fibonacci or Lucas numbers

Punjab University Journal of Mathematics
In this note, we show that there is no Fibonacci number that can be expressed as a concatenation of three Fibonacci or Lucas numbers under a certain constraint. That is, we solve to the Diophantine equations Fn = 10d+lFm1 + 10lFm2 + Fm3 and Fn = 10d+lLm1 + 10lLm2 + Lm3 in non-negative integers (n, m1, m2, m3) with m2 ≤ m1, where d and l represent the ...
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Simple integral representations for the Fibonacci and Lucas numbers

2022
Summary: Integral representations of the Fibonacci numbers \(F_{kn+r}\) and the Lucas numbers \(L_{kn+r}\) are presented. Each is established using methods that rely on nothing beyond elementary integral calculus.
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k-Fibonacci and k-Lucas Numbers as Product of Two Repdigits

Results in Mathematics, 2021
Salah Eddine Rihane
exaly  

On Gauss Fibonacci polynomials, on Gauss Lucas polynomials and their applications

Communications in Algebra, 2020
Engin Özkan
exaly  

Multiplicative dependence between k-Fibonacci and k-Lucas numbers

Periodica Mathematica Hungarica, 2020
Carlos A Gomez, Florian Luca
exaly  

Generalized Lucas polynomials and relationships between the Fibonacci polynomials and Lucas polynomials

Communications in Algebra, 2019
Engin Özkan
exaly