Question 25
Let the sequence \{$a_n$\} be defined as follows:
$$
a_1 = 1
$$
$$
a_2 = 3
$$
$$
a_{n+2} = 2a_{n+1}a_n + 1 \text{; para todo} n \ge 1
$$
Prove that the maximum power of 2 that divides $a_{4006} - a_{4005}$ is $2^{2003}$.
$$
a_1 = 1
$$
$$
a_2 = 3
$$
$$
a_{n+2} = 2a_{n+1}a_n + 1 \text{; para todo} n \ge 1
$$
Prove that the maximum power of 2 that divides $a_{4006} - a_{4005}$ is $2^{2003}$.