斐波那齐数列的整除性质研究

摘要

Several foundational features of Fibonacci number sequence on exact division are proven： （1） To any positive integer, there are infinite items which are multiple of it in Fibonacci number se quence; （2） To any positive integer n, am is the first item after which is multiple of it, then m must be not larger than n2 ; （3） To any positive integer n, a0,am,a2m,a3m,… is the whole items which are multiple of it, where am is the first item after a0 which is multiple of it; （4） To any prime number p, at least one among ap , ap-l and ap＋l of Fibonacci number number sequence must be multiple of it.%给出了斐波那齐数列的若干基本整除性质：（1）任意正整数整除斐波那齐数列中无穷多个项；（2）对于任意正整数n，am。是斐波那齐数列a0后第一个被n整除的项，则m不超过n2；（3）被任意正整数n整除的斐波那齐数列中的项恰好为a0，am，a2m，a3m，…，其中am是斐波那齐数列后第一个被n整除的项；（4）任意一个素数p，必然整除斐波那齐数列中的ap，ap-1，或ap＋1。