Showing a limited preview of this publication:
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.
Keywords.: Fibonacci numbers; Zeckendorf representation
Received: 2009-09-11
Revised: 2009-10-08
Accepted: 2009-10-20
Published Online: 2010-01-26
Published in Print: 2009-December
© de Gruyter 2009
