Geodesic
The 2-adic order of the Tribonacci numbers and the equation \(T_n = m!\)
Journal of integer sequences, Tome 17 (2014) no. 10
Let $(T_{n})_{n \ge 0}$ be the Tribonacci sequence defined by the recurrence $T_{n+2} = T_{n+1} + T_{n} + T_{n-1}$, with $T_{0} = 0$ and $T_{1} = T_{2} = 1$. In this paper, we characterize the 2-adic valuation of $T_{n}$ and, as an application, we completely solve the Diophantine equation $T_{n} = m$!.
Classification : 11B39, 11B50, 11A07
Keywords: tribonacci number, divisibility, 2-adic valuation 
@article{JIS_2014__17_10_a0,
     author = {Marques,  Diego and Lengyel,  Tam\'as},
     title = {The 2-adic order of the {Tribonacci} numbers and the equation {\(T_n} = m!\)},
     journal = {Journal of integer sequences},
     year = {2014},
     volume = {17},
     number = {10},
     zbl = {1372.11017},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2014__17_10_a0/}
}
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Marques,  Diego; Lengyel,  Tamás. The 2-adic order of the Tribonacci numbers and the equation \(T_n = m!\). Journal of integer sequences, Tome 17 (2014) no. 10. http://geodesic.mathdoc.fr/item/JIS_2014__17_10_a0/