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

### Summary

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