There exists a unique strictly increasing sequence of nonnegative integers a_{1}<a_{2}<\cdots<a_{k} such that

\dfrac{2^{289}+1}{2^{17}+1}=2^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{k}}

What is k ?

**Answer Choices**

A. 117

B. 136

C. 137

D. 273

E. 306

There exists a unique strictly increasing sequence of nonnegative integers a_{1}<a_{2}<\cdots<a_{k} such that

\dfrac{2^{289}+1}{2^{17}+1}=2^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{k}}

What is k ?

**Answer Choices**

A. 117

B. 136

C. 137

D. 273

E. 306