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1.
Let P and Q be non-zero relatively prime integers. The Lucas sequence {Un(P,Q)} is defined by
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LI Hai-long LIU Hua-kel.Department of Mathematics Weinan Teacher''''s College Weinan China .College of Mathematics Information Science Henan University Kaifeng China 《数学季刊》2004,19(1):84-89
In this paper, we introduce a new counting function a(m) related to the Lucas number, then use conjecture and induction methods to give an exact formula Ar(N)=α(n), (r=1,2,3) and prove them. 相似文献
4.
Kantaphon Kuhapatanakul 《International Journal of Mathematical Education in Science & Technology》2016,47(5):797-803
In this note, we study the Lucas p-numbers and introduce the Lucas p-triangle, which generalize the Lucas triangle is defined by Feinberg. We derive an expansion for the Lucas p-numbers by using some properties of our triangle. 相似文献
5.
Lucas序列中的平方类 总被引:1,自引:0,他引:1
设Un(a,b)与Vn(a,b)表示参数为a和b的Lucas序列,我们找出了α为偶数, b=±1的Lucas序列的所有非平凡的平方类. 相似文献
6.
In this paper, we show that if (un)n?1 is a Lucas sequence, then the Diophantine equation in integers n?1, k?1, m?2 and y with |y|>1 has only finitely many solutions. We also determine all such solutions when (un)n?1 is the sequence of Fibonacci numbers and when un=(xn-1)/(x-1) for all n?1 with some integer x>1. 相似文献
7.
In 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. 相似文献
8.
利用第一类Chebyshev多项式的性质以及其与Lucas数的关系得到了关于Lucas数立方的一些恒等式. 相似文献
9.
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
10.
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
11.
The degree sequence of Fibonacci and Lucas cubes 总被引:1,自引:0,他引:1
The Fibonacci cube Γn is the subgraph of the n-cube induced by the binary strings that contain no two consecutive 1’s. The Lucas cube Λn is obtained from Γn by removing vertices that start and end with 1. It is proved that the number of vertices of degree k in Γn and Λn is and , respectively. Both results are obtained in two ways, since each of the approaches yields additional results on the degree sequences of these cubes. In particular, the number of vertices of high resp. low degree in Γn is expressed as a sum of few terms, and the generating functions are given from which the moments of the degree sequences of Γn and Λn are easily computed. 相似文献
12.
将二项式系数的性质应用到Lucas数列的研究中,并结合Fibonacci数列与Lucas数列的恒等式得到几个有趣的Lucas数列的同余式. 相似文献
13.
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
14.
F. Arnault. 《Mathematics of Computation》1997,66(218):869-881
We give bounds on the number of pairs with such that a composite number is a strong Lucas pseudoprime with respect to the parameters .
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In this paper we compute the number of curves of genus 2 defined over a finite field k of odd characteristic up to isomorphisms defined over k; the even characteristic case is treated in an ongoing work (G. Cardona, E. Nart, J. Pujolàs, Curves of genus 2 over field of even characteristic, 2003, submitted for publication). To this end, we first give a parametrization of all points in
, the moduli variety that classifies genus 2 curves up to isomorphism, defined over an arbitrary perfect field (of zero or odd characteristic) and corresponding to curves with non-trivial reduced group of automorphisms; we also give an explicit representative defined over that field for each of these points. Then, we use cohomological methods to compute the number of k-isomorphism classes for each point in
. 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