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].     

Fibonacci数列的模数列的周期性

对于Fibonacci数列{Fn}以及给定的正整数m,由Fn关于模m的最小非负剩余an,构成一个新的数列{an},称为Fibonacci数列的模数列.本文利用初等数论的知识和数学归纳法,证明了Fibonacci数列的模数列是周期数列,并且是纯周期数列.     

一类递推数列的周期性

设k,m是适合k>2的正整数,p=2cos(2π)/k.本文证明了:如果数列A={an}n=0∞满足递推关系an+2m=pan+m-an(n≥0),则A是周期数列,它的最小正周期是km的约数.另外,给出了最小正周期小于km的非零数列的例子.     

构造单调数列证明不等式

数列{an}中,如果对任意的n∈N^＊,都有n＋1〉an（或an＋1〈an）,则称{an}为增（或减）数列．本文探求通过构造单调数列来证明与正整数有关的不等式问题．     

初探高考题中的反数列

2010年湖南理科高考第15题为: 若数列{an}满足:对任意的n∈N*,只有有限个正整数m使得am＜n成立,记这样的m的个数为(an)*,则得到一个新数列{an)*}.例如,若数列{an}是1,2,3,…,n,…,则数列{(an)*}是0,1,2,…,n-1,….     

新题征展(113)

A 题组新编 1.(袁保金)在数列{an}中,如果存在非零常数T,使得am+T＝am对于任意的非零自然数m均成立,那么就称数列{an}为周期数列,其中T为数列{an}的周期.     

利用单位根给出一般周期数列的通项公式

首先回顾周期数列的定义:给定数列{an},如果存在不为0的正整数T,使得ai=ai+T对一切自然数i都成立,则称数列{an}称为周期数列,称T为这个数列的周期.例如a,b,c,a,b,c,…,一般要写出这个简单周期数列的通项并不困难,通常可以用分段通项公式来确定.但     

我为高考设计题目

题10 已知数列{an}中,若对任意的正整数n,都有an＋1-an〈an＋2-an＋1成立,则称数列{an}是增差数列．     

一个定理的加强和猜想

文[1]中的定理2为:数列{an}满足an 2=pan 1-an,且p=2cos2πk(k>2,k∈N ),则k是它的一个周期.对该定理我们可作进一步加强得:定理不全为零的数列{an}满足an 2=pan 1-an,且p=2cos2πk(k>2,k∈N ).则该数列具有周期性,且最小正周期为k.证明数列{an}是线性递推数列,则特征方程为x2-     

关于立方阶数列及其两个猜想

对任意正整数n,设{cn}表示立方数列,即cn=n3.而立方阶数列{Zn}定义为最小的正整数Zn使得czn/n≡l(mod cn 1).本文的主要目的是利用初等森研究数列{zn}的计算问题,并给出了Zn的具体表示形式,从而证明了Kenichiro Kashihara提出的两个猜想:A.数列{zn}中除了第一项外,其余项都是偶数与B.在数列{zn}中存在无限多个平方数是正确的.     

关于纤维锥的深度和Hilbert级数

Let (R,m) be a Cohen-Macaulay local ring of dimension d with infinite residue field, I an m-primary ideal and K an ideal containing I. Let J be a minimal reduction of I such that, for some positive integer k, KIn ∩ J = JKIn-1 for n ≤ k ? 1 and λ( JKKIIkk-1 ) = 1. We show that if depth G(I) ≥ d-2, then such fiber cones have almost maximal depth. We also compute, in this case, the Hilbert series of FK(I) assuming that depth G(I) ≥ d - 1.     

Series with monotone coefficients by Walsh system

The paper studies the series $\sum\limits_{n = 0}^\infty {a_n } W_n (x)$ by Walsh system, where |a _n | monotone tends to zero and $\sum\limits_{n = 1}^\infty {a_{_n }^2 } = \infty $ . Some theorems on correction in L ¹ and representability of functions from L ^p , p ∈ (0, 1) by subseries of the Walsh series are proved.     

Remarks on Mean Convergence (Boundedness) of Partial Sums of Trigonometric Series

Fairly general conditions on the coefficients of even and odd trigonometric Fourier series under which L-convergence (boundedness) of partial sums of the series is equivalent to the relation are given.     

On the Stability of the Maximum Term of the Entire Dirichlet Series

We establish necessary and sufficient conditions for the logarithms of the maximum terms of the entire Dirichlet series and to be asymptotically equivalent as Re z → +∞ outside a certain set of finite measure. __________ Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 571–576, April, 2005.     

星扇轮联图的邻点可约边染色

对简单图G(V,E),若存在自然数κ(1≤κ≤Δ(G))和映射f:E(G)→{1,2,…,κ}使得对任意相邻两点u,v∈V(G),uv∈E(G),当d(u)=d(v)时,有C(u)=C(u),则f为G的κ-邻点可约边染色(简记为κ-AVREC of G),而x′_(aur)(G)=max{κ|κ-AVREC of G}称为G的邻点可约边染色数.其中C(u)={f(uv)|uv∈E(G)}.证明了联图在若干情况下的邻点可约边染色定理,得到了S_n+S_n,F_n+F_n,W_n+W_n,S_n+F_n,S_n+W_n和F_n+W_n的邻点可约边色数.     

經驗分佈對理論分佈的比值

<正> 設F(x)是隨機變数X的分佈函數,x_1,x_2,…,x_n是對X的n次相互獨立觀測的結果.將n個數據按照數值從小到大排列起來,以x_k代表其中的第k個,我們把原來的結果寫成     

On a problem of partitions of $$\mathbb {Z}_{m}$$ Z m with the same representation functions

Periodica Mathematica Hungarica - For any positive integer m, let $$\mathbb {Z}_{m}$$ be the set of residue classes modulo m. For $$A\subseteq \mathbb {Z}_{m}$$ and $$\overline{n}\in \mathbb...     

Estimates for Sums of Coefficients of Dirichlet Series with Functional Equation

Suppose we have a Dirichlet series L(s) = _{n = 1} a _n n ^–s such that it, and its twists by Dirichlet characters have analytic continuation and a functional equation of a specific kind. Suppose also that the root numbers of the twists are equidistributed on the unit circle. The purpose of this note is to get an estimate for the quantity for a prime modulus p.We use a modification of the method of Chandrasekharan and Narasimhan and we use in an essential way a Rankin-Selberg type estimate for the average of |a _n|².     

带对称齐次核的级数算子的范数刻画及其应用

对带对称齐次核K(m,n)的级数算子T:T{an}=Σ_(n=1)~∞ K(m,n)an,{an}∈lω(n),l={{an)| an≥0,Σ_(n=1)~∞ω(n)an<+∞},本文研究了T的范数刻画,并讨论其应用.