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On Concatenations of Fibonacci and Lucas Numbers
Bulletin of the Iranian Mathematical Society, 2022Let \( (F_n)_{n\ge 0} \) and \( (L_n)_{n\ge 0} \) be the usual Fibonacci and Lucas sequences defined respectively by the linear recurrence relations: \( F_0=0 \), \( F_1=1 \), \( F_{n+2}=F_{n+1}+F_n \) and \( L_0=2 \), \( L_1=1 \), \( L_{n+2}=L_{n+1}+L_n \) for all \( n\ge 0 \).
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On quaternion‐Gaussian Lucas numbers
Mathematical Methods in the Applied Sciences, 2020In this study, we have considered Gaussian Lucas numbers and given the properties of these numbers. Then, we have defined the quaternions that accept these numbers as coefficients. We have examined whether the numbers defined provide some identities for quaternions in the literature.
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Journal of Philosophical Logic, 1982
Discussion de l'argumentation de J. R. Lucas suivant laquelle les etres humains ne peuvent etre des machines ("Minds, Machines and Godel", Philosophy, 36, 1961, p. 120-124). L'A. montre que l'argument de Lucas suivant lequel il n'est pas une machine repose sur une premisse erronee: suivant l'A., Lucas est donc lui-meme une machine.
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Discussion de l'argumentation de J. R. Lucas suivant laquelle les etres humains ne peuvent etre des machines ("Minds, Machines and Godel", Philosophy, 36, 1961, p. 120-124). L'A. montre que l'argument de Lucas suivant lequel il n'est pas une machine repose sur une premisse erronee: suivant l'A., Lucas est donc lui-meme une machine.
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Perfect fibonacci and lucas numbers
Rendiconti del Circolo Matematico di Palermo, 2000Using elementary means, the author shows that no Fibonacci or Lucas number is perfect.
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On Square Pseudo-Lucas Numbers
Canadian Mathematical Bulletin, 1978J. H. E. Cohn (1) has shown thatare the only square Fibonacci numbers in the set of Fibonacci numbers defined byIf n is a positive integer, we shall call the numbers defined by(1)pseudo-Lucas numbers.
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2021
In the literature, the Fibonacci numbers are usually denoted by \(F_n\), but this symbol is already reserved for the Fermat numbers in this book. So we will denote them by \(K_n\). The sequence of Fibonacci numbers \(\,\,(K_n)_{n=0}^\infty \,\,\) starts with \(K_0=0\) and \(K_1=1\) and satisfies the recurrence.
Michal Křížek +2 more
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In the literature, the Fibonacci numbers are usually denoted by \(F_n\), but this symbol is already reserved for the Fermat numbers in this book. So we will denote them by \(K_n\). The sequence of Fibonacci numbers \(\,\,(K_n)_{n=0}^\infty \,\,\) starts with \(K_0=0\) and \(K_1=1\) and satisfies the recurrence.
Michal Křížek +2 more
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Coding theory on Lucas p numbers
Discrete Mathematics, Algorithms and Applications, 2016In [K. Kuhapatanakul, The Lucas [Formula: see text]-matrix, Internat. J. Math. Ed. Sci. Tech. (2015), http://dx.doi.org/10.1080/0020739X.2015.1026612], Kuhapatanakul introduced Lucas [Formula: see text] matrix, [Formula: see text] whose elements are Lucas [Formula: see text] numbers. In this paper, we developed a new coding and decoding method followed
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Mersenne numbers as a difference of two Lucas numbers
Commentationes Mathematicae Universitatis Carolinae, 2023Summary: Let \((L_n)_{n\geq 0}\) be the Lucas sequence. We show that the Diophantine equation \(L_n-L_m=M_k\) has only the nonnegative integer solutions \((n,m,k)=(2,0,1)\), \((3,1,2)\), \((3,2,1)\), \((4,3,2)\), \((5,3,3)\), \((6,2,4)\), \((6,5,3)\) where \(M_k=2^k-1\) is the \(k\)th Mersenne number and \(n>m\).
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Trisection method by k-Lucas numbers
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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1997
Consider the following number trick–try it out on your friends. You ask them to write down the numbers from 0 to 9. Against 0 and 1 they write any two numbers (we suggest two fairly small positive integers just to avoid tedious arithmetic, but all participants should write the same pair of numbers).
Peter Hilton +2 more
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Consider the following number trick–try it out on your friends. You ask them to write down the numbers from 0 to 9. Against 0 and 1 they write any two numbers (we suggest two fairly small positive integers just to avoid tedious arithmetic, but all participants should write the same pair of numbers).
Peter Hilton +2 more
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