Journal of Mathematics and Statistics

Unique Representation of Positive Integers as a Sum of Distinct Tribonacci Numbers

Salim Badidja and Abdelmadjid Boudaoud

DOI : 10.3844/jmssp.2017.57.61

Journal of Mathematics and Statistics

Volume 13, Issue 1

Pages 57-61


Let (Tm)m≥1 be the tribonacci sequence. We show that every integer N ≥ 1 can be written as a sum of the terms αm Tm, where m runs over the set of strictly positive integers and αm   (m ≥ 1) are either 1 or 0. The previous representation of N is unique if each time that we have αm  = 1 then at least the two coefficients  directly following αm are zero, i.e., αm+1 = αm+2 = 0.


© 2017 Salim Badidja and Abdelmadjid Boudaoud. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.