Results 11 to 20 of about 626,146 (282)

Bi-Periodic (p,q)-Fibonacci and Bi-Periodic (p,q)-Lucas Sequences

Sakarya Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 2023
In this paper, we define bi-periodic (p,q)-Fibonacci and bi-periodic (p,q)-Lucas sequences, which generalize Fibonacci type, Lucas type, bi-periodic Fibonacci type and bi-periodic Lucas type sequences, using recurrence relations of (p,q)-Fibonacci and (p,
Yasemin Taşyurdu, Naime Şeyda Türkoğlu   +1 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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Three new classes of binomial Fibonacci sums [PDF]

Transactions on Combinatorics
In this paper, we introduce three new classes of binomial sums involving Fibonacci (Lucas) numbers and weighted binomial coefficients. One particular result is linked to a problem proposal recently published in the journal The Fibonacci Quarterly.
Robert Frontczak
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Erdos Conjecture I. [PDF]

, 2000
In this short paper I show how it is related to other famous unsolved problems in prime number theory. In order to do this, I formulate the main hypothetical result of this paper - a useful upper bound conjecture (Conjecture 3.), describing one aspect of
Saidak, F.
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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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Diophantine equations with Lucas and Fibonacci number coefficients [PDF]

Notes on Number Theory and Discrete Mathematics
Fibonacci and Lucas numbers are special number sequences that have been the subject of many studies throughout history due to the relations they provide.
Cemil Karaçam, Alper Vural, Bilal Aytepe, Ferhat Yıldız   +3 more
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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, Park Jong-Do, Song Kyunghwan   +2 more
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Lucas numbers of the form PX2, where P is prime

International Journal of Mathematics and Mathematical Sciences, 1991
Let Ln denote the nth Lucas number, where n is a natural number.
Neville Robbins
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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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Mersenne-Lucas hybrid numbers

Mathematica Montisnigri, 2021
We introduce Mersenne-Lucas hybrid numbers. We give the Binet formula, the generating function, the sum, the character, the norm and the vector representation of these numbers. We find some relations among Mersenne-Lucas hybrid numbers, Jacopsthal hybrid numbers, Jacopsthal-Lucas hybrid numbers and Mersenne hybrid numbers.
Engin Özkan, Mine Uysal
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