Results 281 to 290 of about 10,192,155 (339)
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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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Fibonacci numbers as mixed concatenations of Fibonacci and Lucas numbers
Mathematica SlovacaLet (Fn)n≥0 and (Ln)n≥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.
A. Altassan, Murat Alan
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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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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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Power sums of Fibonacci and Lucas numbers
Quaestiones Mathematicae, 2011Polynomial representation formulae for power sums of the extended Fibonacci-Lucas numbers are established, which include, as special cases, four for-mulae for odd power sums of Melham type on Fibonacci and Lucas numbers, obtained recently by Ozeki and Prodinger (2009).Quaestiones Mathematicae 34(2011), 75 ...
CHU, Wenchang, LI N. N.
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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 the order-k generalized Lucas numbers
Applied Mathematics and Computation, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kilic, E, Tasci, D
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1991
In the paper [3], we have proved that the only triangular numbers (i.e., the positive integers of the form \( \frac{1}{2}m \)(m+1)) in the Fibonacci sequence $$ {u_n} + 2 = {u_{n + 1}} + {u_{{n^,}}}{u_0} = 0, {u_1} = 1 $$ are u ±1=u2=1, u4=3, u8=21 and u10=55. This verifies a conjecture of Vern Hoggatt [2].
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In the paper [3], we have proved that the only triangular numbers (i.e., the positive integers of the form \( \frac{1}{2}m \)(m+1)) in the Fibonacci sequence $$ {u_n} + 2 = {u_{n + 1}} + {u_{{n^,}}}{u_0} = 0, {u_1} = 1 $$ are u ±1=u2=1, u4=3, u8=21 and u10=55. This verifies a conjecture of Vern Hoggatt [2].
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A quantum calculus framework for Gaussian Fibonacci and Gaussian Lucas quaternion numbers
Notes on Number Theory and Discrete MathematicsIn order to investigate the relationship between Gaussian Fibonacci numbers and quantum numbers and to develop both a deeper theoretical understanding in this study, q-Gaussian Fibonacci, q-Gaussian Lucas quaternions and polynomials are taken with ...
B. Kuloǧlu
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Data hiding in virtual bit-plane using efficient Lucas number sequences
Multimedia tools and applications, 2020B. Datta, Koushik Dutta, S. Roy
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