Números Tribonacci, S-unidades y triplas diofánticas

• Gómez Ruiz, Carlos Alexis ^[1]
  1. [1] Universidad del Valle
• Localización: Integración: Temas de matemáticas, ISSN 0120-419X, Vol. 33, Nº. 2, 2015 (Ejemplar dedicado a: REVISTA INTEGRACIÓN), págs. 121-133
• Idioma: español
• DOI: 10.18273/revint.v33n2-2015003
• Títulos paralelos:
  • Tribonacci numbers, S-units and diophantine triples
• Enlaces
  • Texto completo (pdf)
• Resumen
  • español

    La sucesión Tribonacci T := {Tn}n≥0 tiene valores iniciales T0 = T1 =0,T2 =1 y cada término posterior es la suma de los tres términos precedentes. En este artículo, estudiamos la ecuación Tn = kTm, donde k es una S-unidad, para un conjunto finito S de primos. Particularmente, mostramos que cualquier par de miembros de la tripla diofántica {9, 56, 103} asociada a T +1, no se puede extender a otra tripla diofántica asociada a T +1.

  • English

    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.

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