Lucas Numbers
On the k–Lucas Numbers of Arithmetic Indexes
... k-Lucas numbers of arithmetic indexes of the form an + r, where n is a natural number and r is less than ...these numbers and particularly the sums of the first k-Lucas numbers, and ...
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New identities involving generalized Fibonacci and generalized Lucas numbers
... generalized Lucas numbers are ...Fibonacci, Lucas, Pell and Pell-Lucas numbers are exhibited including the two identities of Sury and ...
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The upper bound estimation on the spectral norm of r circulant matrices with the Fibonacci and Lucas numbers
... respectively. This paper gives an upper bound estimation of the spectral norm for r-circulant matrices with Fibonacci and Lucas numbers. The result is more accurate than the corresponding results of S Solak ...
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On the spectral norm of r circulant matrices with the Pell and Pell Lucas numbers
... and Lucas numbers [], Bozkurt and Tam have obtained some results belong to determinants and inverses of r-circulant matrices associated with a number sequence [], Shen and Cen have made a similar study by ...
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On the spectral norms of r circulant matrices with the biperiodic Fibonacci and Lucas numbers
... In this paper, we obtain new upper and lower bounds for the spectral norms of the r- circulant matrices Q and L whose entries are the biperiodic Fibonacci and biperiodic Lucas numbers. This study can be ...
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On the Norms of r Hankel Matrices Involving Fibonacci and Lucas Numbers
... In this paper, we firstly define the r -Hankel matrix with entries Fibonacci and Lucas numbers. Then we introduce the Euclidean norm equality and the spectral norm inequalities of these matrices. ...
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On the Norms of r Toeplitz Matrices Involving Fibonacci and Lucas Numbers
... Lots of article have been written so far, which concern estimates for spectral norms of Toeplitz matrices, which have connections with signal and image processing, time series analysis and many other problems [6]-[8]. ...
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Lucas numbers of the form PX2, where P is prime
... Therefore hypothesis implies that is, n=5k for some k, so t-he conclusion follows ftom Theorem 6... * has no solution if.[r] ...
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GENERATING FUNCTIONS FOR PELL AND PELL-LUCAS NUMBERS
... We invite unpublished novel, original, empirical and high quality research work pertaining to recent developments & practices in the area of Computer, Business, Finance, Marketing, [r] ...
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A Note on Stability of a Linear Functional Equation of Second Order Connected with the Fibonacci Numbers and Lucas Sequences
... the Lucas sequences see, ...Fibonacci numbers p 1, q −1, x0 0 and x1 1, the Lucas numbers p 1, q −1, x0 2 and x1 1, the Pell numbers p 2, q −1, x0 0 and x1 1, the Pell-Lucas or ...
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On the norms of circulant and r circulant matrices with the hyperharmonic Fibonacci numbers
... Many authors have investigated the norms of circulant and r-circulant matrices. In [], Solak studied the lower and upper bounds for the spectral norms of circulant matrices with classical Fibonacci and Lucas ...
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On Fibonacci and Lucas Vectors and Quaternions
... vectors, Lucas vectors and their vector products considering two Fibonacci vectors, two Lucas vectors and one of each ...and Lucas vectors with respect to Fibonacci and Lucas ...two ...
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ON THE HYPERBOLIC FIBONACCI MATRIX FUNCTIONS
... In this work we introduce a new class of hyperbolic matrix functions called hyperbolic Fibonacci matrix functions by comparing Binet formulas for the Fibonacci and Lucas numbers to the formulas of classical ...
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Some Sum Formulas of ( s , t ) Jacobsthal and ( s , t ) Jacobsthal Lucas Matrix Sequences
... Fibonacci, Lucas, Pell, Jacobsthal, and Padovan in [1] ...Jacosthal numbers [7]. Jacobsthal and Jacobsthal Lucas numbers are given by the recurrence relations j n = j n − 1 + 2 j n − 2 , j 0 = ...
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On the norms of an r circulant matrix with the generalized k Horadam numbers
... other upper and lower bounds for the spectral norms of r-circulant matrices associated with the k-Fibonacci and k-Lucas numbers, respectively. It is clear that the same study about similar subject can also ...
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On Pell, Pell Lucas, and balancing numbers
... 29. Dujella, A: Diophantine quadruples and Fibonacci numbers. Bull. Kerala Math. Assoc. 1, 133-147 (2004) 30. Washington, LC: Elliptic Curves, Number Theory and Cryptography. Chapman & Hall/CRC, Boca London ...
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Financial Cycles: A Key To Deciphering Seismic Cycles?
... and Lucas numbers can be directly linked to Moon-Sun ...gave Lucas numbers (in terms of solar years) for the following eclipse cycles - Tzolkinex (7 years), Tritos (11 years), Saros (18 ...
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A note on the equation xy+yz=zx
... Using the Gel’fond-Baker method, they proved that all solutions (x, y, z) of (.) satisfy max {x, y, z} < exp(exp(exp())). This upper bound is far beyond the computable scope at present. In this paper, we shall use ...
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On the Diophantine equation x2+p2k+1=4yn
... A Lucas pair is a pair (α,β) of algebraic integers, such that α + β and αβ are nonzero coprime rational integers and α/β is not a root of ...a Lucas pair (α,β) , we define the corresponding sequence of ...
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Sums of Squares of Fibonacci Numbers with Prime Indices
... and Lucas identities involving both Fibonacci and Lucas numbers appeared in various journals [1]-[3] and books [4] [5] over the ...and Lucas numbers with consecutive primes as ...
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