Note on the Representation of Integers as a Sum of Distinct Fibonacci Numbers

摘要

The fact that every positive integer can be represented uniquely as finite sum of distinct nonconsecutive Fibonacci numbers (F-addends), is considered. The asymptotic value of the average of F-addends and the probable least upper bound of F-addends, are given. The greatest lower bound of F-addends and the bound of the number of integers which are representables as F-addends, are estimated.