Differences of Multiple Fibonacci Numbers
Differences of Multiple Fibonacci Numbers
复制标题
多个斐波那契数的差异
DOI：
10.1515/integ.2009.061
复制
发表时间：
2009
影响因子：
0.4
通讯作者：
H. Alpert
中科院分区：
文献类型：
--
作者：
H. Alpert
我们证明了每一个整数都可以唯一地写成Fibonacci数及其加法逆的和，使得每两个同号项的指数相差至少4，每两个异号项的指数相差至少3。此外，没有办法使用更少的术语来将一个数写为Fibonacci数及其加法逆的和。这是一个类似的Zeckendorf表示。
Abstract We show that every integer can be written uniquely as a sum of Fibonacci numbers and their additive inverses, such that every two terms of the same sign differ in index by at least 4 and every two terms of different sign differ in index by at least 3. Furthermore, there is no way to use fewer terms to write a number as a sum of Fibonacci numbers and their additive inverses. This is an analogue of the Zeckendorf representation.