GOMEZ RUIZ, CARLOS ALEXIS. Tribonacci numbers, S-units and diophantine triples. []. , 33, 2, pp.121-133. ISSN 0120-419X.

The Tribonacci sequence T := {T_n}_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 T_n = kT_m, 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

: Tribonacci numbers; diophantine triples; linear forms in logarithms of algebraic numbers.

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