Results 51 to 60 of about 1,420,930 (275)
Fibonacci Numbers and Identities
The Fibonacci Quarterly, 2013 By investigating a recurrence relation about functions, we first give alternative proofs of various identities on Fibonacci numbers and Lucas numbers, and then, make certain well known identities visible via certain trivalent graph associated to the recurrence relation.
Lang, Cheng Lien, Lang, Mong Lung
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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, Deyi Chen, Yong Zhang
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, 2020 In this paper, closed forms of the summation formulas for generalized Fibonacci and Gaussian generalized Fibonacci numbers are presented. Then, some previous results are recovered as particular cases of the present results.
Y. Soykan
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An Alternating Sum of Fibonacci and Lucas Numbers of Order k
Mathematics, 2020 During the last decade, many researchers have focused on proving identities that reveal the relation between Fibonacci and Lucas numbers. Very recently, one of these identities has been generalized to the case of Fibonacci and Lucas numbers of order k ...
Spiros D. Dafnis +2 more
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An inequality for Fibonacci numbers [PDF]
Mathematica Bohemica, 2022 We extend an inequality for Fibonacci numbers published by P. G. Popescu and J. L. Díaz-Barrero in 2006.
Horst Alzer, Florian Luca
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On Mixed Concatenations of Fibonacci and Lucas Numbers Which are Fibonacci Numbers
, 2022 Let $(F_n)_{n\geq 0}$ and $(L_n)_{n\geq 0}$ be the Fibonacci and Lucas sequences, respectively. In this paper we determine all Fibonacci numbers which are mixed concatenations of a Fibonacci and a Lucas numbers. By mixed concatenations of $ a $ and $ b $, we mean the both concatenations $\overline{ab}$ and $\overline{ba}$ together, where $ a $ and $ b $
Altassan, Alaa, Alan, Murat
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Fibonacci factoriangular numbers
Indagationes Mathematicae, 2017 Abstract Let ( F m ) m ≥ 0 be the Fibonacci sequence given by F 0 = 0 , F 1 = 1 and F m + 2 = F m + 1 + F m , for all m ≥ 0 . In Castillo (2015), it is conjectured that 2 , 5 and 34 are the only Fibonacci numbers of the form n ! + n
Florian Luca +2 more
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Generalized Fibonacci Numbers and Blackwell's Renewal Theorem
, 2010 We investigate a connection between generalized Fibonacci numbers and renewal theory for stochastic processes. Using Blackwell's renewal theorem we find an approximation to the generalized Fibonacci numbers.
Asmussen +9 more
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Determinants and inverses of circulant matrices with complex Fibonacci numbers
Special Matrices, 2015 Let ℱn = circ (︀F*1 , F*2, . . . , F*n︀ be the n×n circulant matrix associated with complex Fibonacci numbers F*1, F*2, . . . , F*n. In the present paper we calculate the determinant of ℱn in terms of complex Fibonacci numbers.
Altınışık Ercan +2 more
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On the Norms of Circulant and $r-$Circulant Matrices With the Hyperharmonic Fibonacci Numbers
, 2015 In this paper, we study norms of circulant and $r-$circulant matrices involving harmonic Fibonacci and hyperharmonic Fibonacci numbers.
Kizilateş, Can, Tuglu, Naim
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