Question 99
Let $\{x_n\}$ be a sequence of integers such that $x_0 = a$, $x_1 = 3$ and
$$
x_n = 2x_{n-1} - 4x_{n-2} + 3 \text{ for all } n \gt 1.
$$
Determine the largest integer $k$ for which there exists a prime $p$ such that $p^k$ divides $x_{2011} - 1$.
$$
x_n = 2x_{n-1} - 4x_{n-2} + 3 \text{ for all } n \gt 1.
$$
Determine the largest integer $k$ for which there exists a prime $p$ such that $p^k$ divides $x_{2011} - 1$.