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
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.