Results 51 to 60 of about 1,200,406 (213)
Fibonacci or Lucas numbers that are products of two Lucas numbers or two Fibonacci numbers [PDF]
, 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 ...
Emin, Ahmet, Daşdemir, Ahmet
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Restricted Permutations, Fibonacci Numbers, and k-generalized Fibonacci Numbers
, 2002 A permutation $π\in S_n$ is said to {\it avoid} a permutation $σ\in S_k$ whenever $π$ contains no subsequence with all of the same pairwise comparisons as $σ$. For any set $R$ of permutations, we write $S_n(R)$ to denote the set of permutations in $S_n$ which avoid every permutation in $R$.
Egge, Eric S., Mansour, Toufik
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Circulants and the factorization of the Fibonacci–like numbers [PDF]
, 2006 summary:Several authors gave various factorizations of the Fibonacci and Lucas numbers. The relations are derived with the help of connections between determinants of tridiagonal matrices and the Fibonacci and Lucas numbers using the Chebyshev ...
Trojovský, Pavel, Seibert, Jaroslav
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On Matrices with Bidimensional Fibonacci Numbers
Annales Mathematicae SilesianaeIn this paper, the bidimensional extensions of the Fibonacci numbers are explored, along with a detailed examination of their properties, characteristics, and some identities.
Costa Eudes Antonio +1 more
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Noûs, Volume 60, Issue 3, Page 593-605, September 2026.ABSTRACT It is a truism of mathematics that differences between isomorphic number systems are irrelevant to arithmetic. This truism is deeply rooted in the modern axiomatic method and underlies most strands of arithmetical structuralism, the view that arithmetic is about some abstract number structure.
Balthasar Grabmayr
wiley +1 more source
Some properties and extended Binet’s formula for the class of bifurcating Fibonacci sequence
Ratio MathematicaOne of the generalizations of Fibonacci sequence is a -Fibonacci sequence, which is further generalized in several other ways, some by conserving the initial conditions and others by conserving the related recurrence relation.
Daksha Manojbhai Diwan +2 more
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Perfect numbers and Fibonacci primes (I) [PDF]
International Journal of Number Theory, 2014 In this paper, we introduce the concept of F-perfect number, which is a positive integer n such that ∑d|n,d<n d2 = 3n. We prove that all the F-perfect numbers are of the form n = F2k-1 F2k+1, where both F2k-1 and F2k+1 are Fibonacci primes. Moreover, we obtain other interesting results and raise a new conjecture on perfect numbers.
Tianxin Cai, Liuquan Wang, Yong Zhang
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Advanced Science, Volume 13, Issue 44, 7 August 2026.ABSTRACT Large‐ion (K, Na) battery systems mitigate uneven global lithium distribution, while their ability to attain recharge time shorter than refueling would remove the final barrier for secondary batteries to replace petroleum vehicles. However, their large‐ion chemistry makes ultra‐fast charging an even significant challenge.
Shukai Ding +12 more
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Discrete Mathematics, 1997 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On Matrix‐Based Cryptography Using Matrix Norm and Special Integer Sequences
Mathematische Nachrichten, Volume 299, Issue 8, Page 2087-2102, August 2026.ABSTRACT In this paper, a novel matrix‐based encryption approach based on the Affine Hill cipher is presented. The key matrix is constructed using the Narayana integer sequence, and the Frobenius norm of the key matrix is used as a scaling factor in the key construction.
Melih Göcen +1 more
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