Marques, Diego; Lengyel, Tamás

The 2-adic order of the tribonacci numbers and the equation $T_n = m!$

J. Integer Seq. 17(10), Article 14.10.1, 8 p., electronic only (2014)


Summary: 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 $T_{n} = m$!.

Mathematics Subject Classification

11B39, 11B50, 11A07


tribonacci number, divisibility, 2-adic valuation