Revista Integración, temas de matemáticas.

Revista Integración, temas de matemáticas

Vol. 33 No. 2 (2015): Revista Integración
Research and Innovation Articles

Tribonacci numbers, S-units and diophantine triples

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  • Carlos Alexis Gómez Ruiz
Carlos Alexis Gómez Ruiz
Universidad del Valle
DOI: https://doi.org/10.18273/revint.v33n2-2015003

Published 2015-12-04

Keywords

  • Tribonacci numbers,
  • diophantine triples,
  • linear forms in logarithms of algebraic numbers.

How to Cite

Gómez Ruiz, C. A. (2015). Tribonacci numbers, S-units and diophantine triples. Revista Integración, Temas De matemáticas, 33(2), 121–133. https://doi.org/10.18273/revint.v33n2-2015003

Abstract

The Tribonacci sequence T := {Tn}n≥0 has initial values T0 = T1 =0, T2 =1 and each term afterwards is the sum of the preceding three terms. In this paper, we study the equation Tn = kTm, where k is an S-unit, for a finite set S of primes. In particular, we show that any two members of the diophantine triple {9, 56, 103} associated to T +1, can not be extended to other diophantine triple associated to T +1.

To cite this article: C.A. Gómez Ruiz, Números Tribonacci, S-unidades y triplas diofánticas, Rev Integr. Temas Mat. 33 (2015), No. 2, 121–133.

 
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