Unique Representation of Positive Integers as a Sum of Distinct Tribonacci Numbers
Salim Badidja1 & Abdelmadjid Boudaoud1 Show affiliations
- University of Mohamed BOUDIAF of M’sila, Algeria
Journal of Mathematics and Statistics, Volume 13, Issue 1, pp. 57–61 · doi.org/10.3844/jmssp.2017.57.61
Abstract
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.
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Badidja, S. & Boudaoud, A. (2017). Unique Representation of Positive Integers as a Sum of Distinct Tribonacci Numbers. Journal of Mathematics and Statistics, 13(1), 57–61. https://doi.org/10.3844/jmssp.2017.57.61
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