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

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Keywords

  • Linear Recurrent Sequences
  • Tribonacci Numbers
  • Representation of Integers