Results 11 to 20 of about 78,268 (260)
ALTERED NUMBERS OF LUCAS NUMBER SQUARED
Journal of Scientific Reports-A, 2023 We investigate two types altered Lucas numbers denoted and defined by adding or subtracting a value from the square of the Lucas numbers. We achieve these numbers form as the consecutive products of the Fibonacci numbers. Therefore, consecutive sum-subtraction relations of altered Lucas numbers and their Binet-like formulas are given by using ...
Fikri KÖKEN, Emre KANKAL
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On square Tribonacci Lucas numbers
Hacettepe Journal of Mathematics and Statistics, 2021 The Tribonacci-Lucas sequence {Sn}{Sn} is defined by the recurrence relation Sn+3=Sn+2+Sn+1+SnSn+3=Sn+2+Sn+1+Sn with S0=3, S1=1, S2=3.S0=3, S1=1, S2=3. In this note, we show that 11 is the only perfect square in Tribonacci-Lucas sequence for n≢1(mod32)n≢1(mod32) and n≢17(mod96).n≢17(mod96).
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Formulae of the Frobenius number in relatively prime three Lucas numbers [PDF]
Songklanakarin Journal of Science and Technology (SJST), 2020 In this paper, we find the explicit formulae of the Frobenius number for numerical semigroups generated by relatively prime three Lucas numbers 2 , L L i i and Lil for given integers i ≥ 3, l ≥ 4 .
Ratchanok Bokaew +2 more
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Hybrid Numbers with Fibonacci and Lucas Hybrid Number Coefficients
Universal Journal of Mathematics and Applications, 2023 In this paper, we introduce hybrid numbers with Fibonacci and Lucas hybrid number coefficients. We give the Binet formulas, generating functions, and exponential generating functions for these numbers. Then we define an associate matrix for these numbers.
Emrah Polatlı
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Fibonacci numbers and Lucas numbers in graphs
Discrete Applied Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mariusz Startek +2 more
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Square-free Lucas d-pseudoprimes and Carmichael-Lucas numbers [PDF]
Czechoslovak Mathematical Journal, 2007 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Carlip, W., Somer, L.
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A Combinatorial Proof of a Result on Generalized Lucas Polynomials
Demonstratio Mathematica, 2016 We give a combinatorial proof of an elementary property of generalized Lucas polynomials, inspired by [1]. These polynomials in s and t are defined by the recurrence relation 〈n〉 = s〈n-1〉+t〈n-2〉 for n ≥ 2.
Laugier Alexandre, Saikia Manjil P.
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On the reciprocal sum of the fourth power of Fibonacci numbers
Open Mathematics, 2022 Let fn{f}_{n} be the nnth Fibonacci number with f1=f2=1{f}_{1}={f}_{2}=1. Recently, the exact values of ∑k=n∞1fks−1⌊{\left({\sum }_{k=n}^{\infty }\frac{1}{{f}_{k}^{s}}\right)}^{-1}⌋ have been obtained only for s=1,2s=1,2, where ⌊x⌋\lfloor x\
Hwang WonTae +2 more
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Fibonacci or Lucas numbers that are products of two Lucas numbers or two Fibonacci numbers
, 2023 This contribution presents all possible solutions to the Diophantine equations $F_k=L_mL_n$ and $L_k=F_mF_n$. To be clear, Fibonacci numbers that are the product of two arbitrary Lucas numbers and Lucas numbers that are the product of two arbitrary Fibonacci numbers are determined herein.
Daşdemir, Ahmet, Emin, Ahmet
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Incomplete Tribonacci–Lucas Numbers and Polynomials [PDF]
Advances in Applied Clifford Algebras, 2014 In this paper, we define Tribonacci-Lucas polynomials and present Tribonacci-Lucas numbers and polynomials as a binomial sum. Then, we introduce incomplete Tribonacci-Lucas numbers and polynomials. In addition we derive recurrence relations, some properties and generating functions of these numbers and polynomials. Also, we find the generating function
Yilmaz, Nazmiye, Taskara, Necati
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