摘要
对任意正整数n,设{c_n}表示立方数列,即c_n=n^3.而立方阶数列{z_n}定义为最小的正整数z_n使得c_n^(zn)≡1(mod c_(n+1)).本文的主要目的是利用初等方法研究数列{z_n}的计算问题,并给出了z_n的具体表示形式,从而证明了Kenichiro Kashihara提出的两个猜想:A.数列{z_n}中除了第一项外,其余项都是偶数与B.在数列{z_n}中存在无限多个平方数是正确的.
For any positive integer n, let {cn} be the cubic number sequence cn = n^3. The cubic order sequence is given by {zn ： zn is the smallest positive integer solution of cn^zn≡ 1 （rood cn＋1）}. The main purpose of this paper is using the elementary method to give an exact expression for zn, then prove that the two conjectures： A. All terms except the first term in sequence {zn} are even and B. There are infinitely many square numbers in {zn} which are proposed by Kenichiro Kashihara are correct.
出处
《纯粹数学与应用数学》
CSCD
北大核心
2008年第3期430-432,共3页
Pure and Applied Mathematics
基金
国家自然科学基金(10671155)
关键词
立方阶数列
同余性质
猜想
the cubic order sequence, congruence, conjecture
