Simple solution hidden deep within

Algebra Level 3

Which of the following is equivalent to

$(x+1)(x^{2} + 1)(x^{4} + 1)(x^{8} + 1)...(x^{65536} + 1)$ ?

x^{131072} + x^{65536} + ... + x^{2} + 1

\frac{x^{131072} + 1}{x + 1}

x^{131072} - 1

\frac{x^{131072} - 1}{x - 1}