Question 19
There exists a unique strictly increasing sequence of nonnegative integers $a_1 \lt a_2 \lt \cdots \lt a_k$ such that $$
\frac{2^{289} + 1}{2^{17} + 1} = 2^{a_1} + 2^{a_2} + \cdots + 2^{a_k}.
$$ What is $k?$
\frac{2^{289} + 1}{2^{17} + 1} = 2^{a_1} + 2^{a_2} + \cdots + 2^{a_k}.
$$ What is $k?$