Чебьццев多项式与Fibonacci及Lucas多项式

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。     

一些包含Fibonacci-Lucas数的恒等式和同余式

给出了一些包含F ibonacci-Lucas数的恒等式和同余式.     

关于Lucas三角形猜想的一个结果

运用初等方法,证明k=7时Lucas三角形不存在.     

Fibonacci数列倒数的无穷和

利用初等方法以及取整函数的性质研究了Fibonacci数列三次倒数的求和问题,获得了该和式倒数取整后的确切值,也就是给出了一个包含Fibonacci数列有趣的恒等式.     

关于FIBONACCI数列的注记

关于ＦＩＢＯＮＡＣＣＩ数列的注记＊陈木法（北京师范大学数学系１００８７５）新近的文［１］和［２］研究了Ｆｉｂｏｎａｃｃｉ数列（简称为Ｆ数列）的一些性质，笔者发现这些结果大多容易从文［３］的两条基本性质导出．因而略作说明所谓Ｆ数列，乃是Ｆ０＝０，Ｆ１＝...     

Fibonacci数列模p~r的周期性研究

对任意素数p、正整数r,Fibonacci数列{Fn}对pr取模构成一个数列{an}.若{Fn}的最小正周期为T,则{an}的最小正周期为pr-1T,首次提出该定理,并用数学归纳法进行了证明.此外对任意正整数m,不加证明地给出了{Fmod m}的周期性定理.     

Fibonacci数列的模数列的周期的一个性质

Fibonacci数列的模数列是周期数列,并且是纯周期数列.利用模数列的定义,讨论了Fibonacci数列的模数列的周期的一个性质,证明了下列结果:假设m1与m2为不同的正整数,Fibonacci数列{Fn}的模数列{an(m1)}与{an(m2)}的最小正周期分别为T1与T2,则模数列{an([m1,m2])}的最小正周期为[T1,T2].     

广义Fibonacci等距子列关于模L_m的模数列的周期

给出广义Fibonacci等距子列的定义,推导出此类等距子列的统一递推公式,并由此得出其关于Lucas数为模的模数列的周期规律.     

关于Pell数列的Ribenboim问题

本文证明了：第一类Pell数列仅有平方类（1，169），第二类Pell数列没有平方类。     

一些包含Lucas数的恒等式

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.     

Generalized Lucas polynomials and relationships between the Fibonacci polynomials and Lucas polynomials

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.     

On matrices related with Fibonacci and Lucas numbers

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.     

The Lucas p-matrix

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.     

Some new Fibonacci and Lucas identities by matrix methods

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.     

Fibonacci and Lucas congruences and their applications

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.     

涉及广义Fibonacci-Lucas数的幂的一些级数的近似值

计算出涉及广义Fibonacci-Lucas数的幂的一些级数的近似值。