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ISSN: 1549-3644 (Print)
ISSN: 1558-6359 (Online)
Research Article Open Access

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

Salim Badidja1 and Abdelmadjid Boudaoud1
  • 1 University of Mohamed BOUDIAF of M’sila, Algeria

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.

Journal of Mathematics and Statistics
Volume 13 No. 1, 2017, 57-61

DOI: https://doi.org/10.3844/jmssp.2017.57.61

Submitted On: 28 December 2016 Published On: 16 March 2017

How to Cite: 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

Open AccessCopyright: © 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.

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Keywords

  • Linear Recurrent Sequences
  • Tribonacci Numbers
  • Representation of Integers