Lucas number
New identities involving generalized Fibonacci and generalized Lucas numbers
... In this paper, we have derived two new formulae involving the two kinds of generalized numbers, namely, generalized Fibonacci and generalized Lucas numbers. Some special formulae involving the celebrated numbers ...
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On the k–Lucas Numbers of Arithmetic Indexes
... In this paper, we study the k-Lucas numbers of arithmetic indexes of the form an + r, where n is a natural number and r is less than r. We prove a formula for the sum of these numbers and particularly the ...
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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 and S ...
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On quaternions with generalized Fibonacci and Lucas number components
... Iyer [] gave some relations connecting the Fibonacci and Lucas quaternions. In [], Swamy derived the relations of generalized Fibonacci quaternions. Iakin [, ] intro- duced the concept of a higher order ...
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A new generalization of convolved (p,q)−Fibonacci and (p,q)−Lucas polynomials
... The multiple sum of Fibonacci numbers have been studied several papers in [8, 20, 21]. In this section, we consider the some mixed–multiple sums for (p, q)−Fibonacci and ( p, q)−Lucas polynomials by applying the ...
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2is analyzed for its patterns of non-zero distinct integral solutions
... Abstract: The sextic non-homogeneous equation with four unknowns represented by the Diophantine equation x 3 y 3 2 ( k 2 3 ) z 5 w is analyzed for its patterns of non-zero distinct integral solutions are ...
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Bicomplex Tetranacci and Tetranacci-Lucas Quaternions
... In this paper, we define bicomplex Tetranacci and bicomplex Tetranacci-Lucas quaternions by combining bicomplex numbers and Tetranacci, Tetranacci-Lucas numbers and give some properties of them. Before ...
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On the Lucas polynomials and some of their new identities
... Ma and Zhang [3] used the properties of Chebyshev polynomials to obtain some identi- ties involving Fibonacci numbers and Lucas numbers. Wang and Zhang [4] proved some divisible properties involving Fibonacci ...
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INTEGRAL SOLUTIONS OF NON- HOMOGENEOUS QUINTIC EQUATION WITH THREE UNKNOWNS
... Jacobsthal-Lucas number,Pronic numbers, Stella octangular numbers, Octahedral numbers, Centered Polygonal numbers, Centered Pentagonal Pyramidal numbers, Centered Hexagonal Pyramidal numbers, Generalized ...
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On Fibonacci and Lucas Vectors and Quaternions
... called Lucas numbers were introduced by Edouard Lucas, a French mathematician, in 1878 and they also became a widely studied subject of mathematics ...
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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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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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Face detection and tracking at different angles in video using optical flow
... a number of issues including the real time face feature tracking under a variety of imaging conditions ...Pyramidal Lucas-Kanade Feature Tracker algorithm [4] is used. Pyramidal Lucas Kanade ...
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Robust decision theory and the Lucas critique
... A number of economists seem to regard the Critique as valid (almost without question) and indeed it has, at least in part, been responsible for stimulat- ing entirely new methodological paradigms such as ...
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Process alignment in focused factories; an international comparison between eye hospitals, focused on the cataract process
... In compliance with the mission of providing high quality patient care, community outreach, graduate and continuing medical education and scientific research, The New York Eye and Ear Infirmary has built upon its ...
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Behind the T(rope): One Boxer's Story
... corner. Lucas, the second author of the article, is known around the gym as a local boxing ...approaches Lucas, playfully swatting the air around him, urging him to get up and swing ...releases Lucas ...
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A NEW GENERALIZATION OF FIBONACCI AND LUCAS TYPE SEDENIONS
... q Lucas sedenions which are de…ned by means of the q ...q Lucas sedenions such as Binet-Like formulas, exponential generating functions, summation formulas, Cassini’s identities, Catalan’s identities and ...
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Shifted powers in Lucas Lehmer sequences
... Abstract. We develop a general framework for finding all perfect powers in sequences derived by shifting non-degenerate quadratic Lucas-Lehmer binary recurrence sequences by a fixed integer. By combining this ...
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A generalization of Lucas' theorem to vector spaces
... We employ this family to generalize to vector-valued abstract polynomials in vector spaces the classical Lucas’ theorem on the zeros of the derivative of a polynomial and a theorem due t[r] ...
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A NOTE ON HORADAM HYBRINOMIALS
... Motivated by some of the above-cited recent works, we introduce here new polynomials which are called Horadam hybrinomials. Our de…nitions give rise to a more general hybrid polynomial sequence by receiving components ...
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