Fibonacci数的整除性

The Divisibility of Fibonacci Number

设F1=F2=1,则称满足递推关系Fn=Fn-1+Fn-2,n≥3的数列{Fn}(n=1,2,3,…)为Fibonacci数列,其中任意一个数Fn称为Fibonacci数.该文主要研究Fibonacci数的整除性质,得到一个一般性的结果.

Let F1 = F2 = 1, the sequence { Fn} （ n = 1,2,3, …… ） with the recurrence retetion Fn= Fn-1 ＋ Fn-2, n≥3 is called Fibonacci sequence. For each fixed n, F, is called a Fibonacci number. In this paper, we mainly study the divisibility of Fibonacci number. A general result of the divisibility of Fibonacci number is obtained.