Geodesic
Tribonacci numbers and the Brocard-Ramanujan equation
Journal of integer sequences, Tome 19 (2016) no. 4.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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 
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     author = {Fac\'o, Vin{\'\i}cius and Marques, Diego},
     title = {Tribonacci numbers and the {Brocard-Ramanujan} equation},
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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/