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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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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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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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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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Trisection method by k-Lucas numbers
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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Mersenne Numbers in Generalized Lucas Sequences
Proceedings of the Bulgarian Academy of SciencesLet $$k \geq 2$$ be an integer and let $$(L_{n}^{(k)})_{n \geq 2-k}$$ be the $$k$$-generalized Lucas sequence with certain initial $$k$$ terms and each term afterward is the sum of the $$k$$ preceding terms. Mersenne numbers are the numbers of the form $$2^a-1$$, where $$a$$ is any positive integer.
Altassan, Alaa, ALAN, Murat
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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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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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Lucas-Sierpiński and Lucas-Riesel Numbers
The Fibonacci Quarterly, 2011Daniel Baczkowski +2 more
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