\,2^16 - 1 is divisible by -

Answer: Option C

$$\begin{array}{rl}& \Rightarrow 2^{16}-1\\ & =\left(2^8-1^8\right)\left(2^8+1^8\right)\\ & =\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)\\ & =\left(16-1\right)\left(16+1\right)\left(2^8+1\right)\\ & =15\times 17\left(2^8+1\right)\\ & \therefore 2^{16}-1\text{is divisible by 17}\end{array}$$