共查询到18条相似文献,搜索用时 62 毫秒
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给出了一些包含F ibonacci-Lucas数的恒等式和同余式. 相似文献
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关于收敛的P—级数和的近似值 总被引:4,自引:0,他引:4
当p>1时,p-级数sum from n≥1n 1/p是收敛的.若取p=2,是著名的Bernoulli级数.早在17世纪,由Euler用代数方程与三角函数方程进行类比的方法,给出了 相似文献
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This note provides the some sum formulas for generalized Fibonacci numbers. The results are proved using clever rearrangements, rather than using induction. 相似文献
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利用组合数学的方法,得到了一些包含高阶Genocchi数和广义Lucas多项式的恒等式,并且由此建立了Fibonacci数与Riemann Zeta函数的关系式. 相似文献
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利用初等方法研究Chebyshev多项式的性质,建立了广义第二类Chebyshev多项式的一个显明公式,并得到了一些包含第一类Chebyshev多项式,第一类Stirling数和Lucas数的恒等式. 相似文献
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发现Чебьццев多项式更多的性质。指出并阐明它们与现今流行的Fibonacd及I..ucas多项式的本质上的同一性。 相似文献
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In this article, we find elements of the Lucas polynomials by using two matrices. We extend the study to the n-step Lucas polynomials. Then the Lucas polynomials and their relationship are generalized in the paper. Furthermore, we give relationships between the Fibonacci polynomials and the Lucas polynomials. 相似文献
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LIU Duan-sen LI Chao YANG Cun-dianInstitute of Mathematics Shangluo Teacher''''s College Shangluo China 《数学季刊》2004,19(1):67-68
By studying the properties of Chebyshev polynomials, some specific and meaningful identities for the calculation of square of Chebyshev polynomials, Fibonacci numbers and Lucas numbers are obtained. 相似文献
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In this paper we obtain some new identities containing Fibonacci and Lucas numbers. These identities allow us to give some
congruences concerning Fibonacci and Lucas numbers such as L
2mn+k
≡ (−1)(m+1)n
L
k
(mod L
m
), F
2mn+k
≡ (−1)(m+1)n
F
k
(mod L
m
), L
2mn+k
≡ (−1)
mn
L
k
(mod F
m
) and F
2mn+k
≡ (−1)
mn
F
k
(mod F
m
). By the achieved identities, divisibility properties of Fibonacci and Lucas numbers are given. Then it is proved that there
is no Lucas number L
n
such that L
n
= L
2
k
t
L
m
x
2 for m > 1 and k ≥ 1. Moreover it is proved that L
n
= L
m
L
r
is impossible if m and r are positive integers greater than 1. Also, a conjecture concerning with the subject is given. 相似文献
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Refik Keskin 《International Journal of Mathematical Education in Science & Technology》2013,44(3):379-387
The aim of this article is to characterize the 2 × 2 matrices X satisfying X 2 = X + I and obtain some new identities concerning with Fibonacci and Lucas numbers. 相似文献
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Kantaphon Kuhapatanakul 《International Journal of Mathematical Education in Science & Technology》2013,44(8):1228-1234
In this note, we study the Fibonacci and Lucas p-numbers. We introduce the Lucas p-matrix and companion matrices for the sums of the Fibonacci and Lucas p-numbers to derive some interesting identities of the Fibonacci and Lucas p-numbers. 相似文献
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Predrag Stanimirovi Jovana Nikolov Ivan Stanimirovi 《Discrete Applied Mathematics》2008,156(14):2606-2619
We define the matrix of type s, whose elements are defined by the general second-order non-degenerated sequence and introduce the notion of the generalized Fibonacci matrix , whose nonzero elements are generalized Fibonacci numbers. We observe two regular cases of these matrices (s=0 and s=1). Generalized Fibonacci matrices in certain cases give the usual Fibonacci matrix and the Lucas matrix. Inverse of the matrix is derived. In partial case we get the inverse of the generalized Fibonacci matrix and later known results from [Gwang-Yeon Lee, Jin-Soo Kim, Sang-Gu Lee, Factorizations and eigenvalues of Fibonaci and symmetric Fibonaci matrices, Fibonacci Quart. 40 (2002) 203–211; P. Staˇnicaˇ, Cholesky factorizations of matrices associated with r-order recurrent sequences, Electron. J. Combin. Number Theory 5 (2) (2005) #A16] and [Z. Zhang, Y. Zhang, The Lucas matrix and some combinatorial identities, Indian J. Pure Appl. Math. (in press)]. Correlations between the matrices , and the generalized Pascal matrices are considered. In the case a=0,b=1 we get known result for Fibonacci matrices [Gwang-Yeon Lee, Jin-Soo Kim, Seong-Hoon Cho, Some combinatorial identities via Fibonacci numbers, Discrete Appl. Math. 130 (2003) 527–534]. Analogous result for Lucas matrices, originated in [Z. Zhang, Y. Zhang, The Lucas matrix and some combinatorial identities, Indian J. Pure Appl. Math. (in press)], can be derived in the partial case a=2,b=1. Some combinatorial identities involving generalized Fibonacci numbers are derived. 相似文献
18.
Extending previous searches for prime Fibonacci and Lucas numbers, all probable prime Fibonacci numbers have been determined for and all probable prime Lucas numbers have been determined for . A rigorous proof of primality is given for and for numbers with , , , , , , , , the prime having 3020 digits. Primitive parts and of composite numbers and have also been tested for probable primality. Actual primality has been established for many of them, including 22 with more than 1000 digits. In a Supplement to the paper, factorizations of numbers and are given for as far as they have been completed, adding information to existing factor tables covering .