Results 181 to 190 of about 1,051 (219)
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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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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 matrices related with Fibonacci and Lucas numbers
Applied Mathematics and Computation, 2008In this paper, we obtain some new results on matrices related with Fibonacci numbers and Lucas numbers. Also, we derive the relation between Pell numbers and its companion sequence by using our representations.
Xudan Fu, Xia Zhou
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On Fibonacci search method with k-Lucas numbers
Applied Mathematics and Computation, 2003zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yildiz, B, Karaduman, E
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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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INTRA RATIOS OF FIBONACCI AND LUCAS NUMBERS
JP Journal of Algebra, Number Theory and Applications, 2015Summary: We study the ratios of any \(k\) spacing apart Fibonacci numbers and Lucas numbers as well as intra ratios \(L_n/F_{n\pm k}\) by means of semisimple continued fraction. And the semisimple continued fractions will be applied to solve certain systems of linear equation.
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The continuous functions for the Fibonacci and Lucas p-numbers
Chaos, Solitons & Fractals, 2006zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Stakhov, Alexey, Rozin, Boris
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Incomplete Fibonacci and Lucas numbers
Rendiconti del Circolo Matematico di Palermo, 1996It is well known that the Fibonacci numbers \(F_n\) and the Lucas numbers \(L_n\) can be written as \[ \begin{aligned} F_n &= \sum^k_{i=0} {{n-1-i} \choose i}, \qquad \lfloor (n- 1)/2 \rfloor\leq k\leq n-1, \tag{1}\\ L_n &= \sum^k_{i=0} {n\over {n-i}} {{n-i} \choose i}, \qquad \lfloor n/2 \rfloor \leq k\leq n-1.
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Repdigits as sums of four Fibonacci or Lucas numbers
J. Integer Seq., 2018The Fibonacci sequence \((F_n)_{n\ge 0}\), is defined by the linear recurrence \(F_0=0\), \(F_1=1\), and \(F_{n+2}=F_{n+1}+ F_n\) for all \(n\ge 0\). The Lucas sequence \((L_n)_{n\ge 0}\), is defined by the same recurrence but with different initial terms, \(L_0=2\) and \(L_1=1\).
Benedict Vasco Normenyo +2 more
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Identities for Products of Fibonacci and Lucas Numbers
The Fibonacci Quarterly, 1967Daykin, D. E., Dresel, L. A. G.
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