Question 149
A sequence is defined as follows:
$$
\left\{\begin{array}{l}
u_{0}=15,\ u_{1}=57 \\
u_{n}=u_{n-1}+u_{n-2}\ \text{ for all } n \geq 2
\end{array}\right.
$$
Find the largest integer $k$ such that $3^{k} \mid u_{2017}$.
$$
\left\{\begin{array}{l}
u_{0}=15,\ u_{1}=57 \\
u_{n}=u_{n-1}+u_{n-2}\ \text{ for all } n \geq 2
\end{array}\right.
$$
Find the largest integer $k$ such that $3^{k} \mid u_{2017}$.