Question 21
There exists a unique strictly increasing sequence of nonnegative integers $a_1<a_2<\cdots<a_k$ 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 $k?$