Geodesic
Tribonacci numbers and the Brocard-Ramanujan equation
Journal of integer sequences, Tome 19 (2016) no. 4
Let $(T_{n})_{n\ge 0}$ be the Tribonacci sequence defined by the recurrence $T_{n+2} = T_{n} + T_{n+1}$, with $T_{0} = 0$ and $T_{1} = T_{2} = 1$. In this short note, we prove that there are no integer solutions $(u, m)$ to the Brocard-Ramanujan equation $m! + 1 = u^{2}$ where $u$ is a Tribonacci number.
Classification : 11B39, 11Dxx
Keywords: Fibonacci number, p-adic order, tribonacci number, brocard-Ramanujan equation 
@article{JIS_2016__19_4_a2,
     author = {Fac\'o,  Vin{\'\i}cius and Marques,  Diego},
     title = {Tribonacci numbers and the {Brocard-Ramanujan} equation},
     journal = {Journal of integer sequences},
     year = {2016},
     volume = {19},
     number = {4},
     zbl = {1415.11028},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a2/}
}
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Facó,  Vinícius; Marques,  Diego. Tribonacci numbers and the Brocard-Ramanujan equation. Journal of integer sequences, Tome 19 (2016) no. 4. http://geodesic.mathdoc.fr/item/JIS_2016__19_4_a2/