TY  - JOUR
AU  - Badidja, Salim 
AU  - Boudaoud, Abdelmadjid 
PY  - 2017
TI  - Unique Representation of Positive Integers as a Sum of Distinct Tribonacci Numbers
JF  - Journal of Mathematics and Statistics
VL  - 13
IS  - 1
DO  - 10.3844/jmssp.2017.57.61
UR  - https://thescipub.com/abstract/jmssp.2017.57.61
AB  - 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.