Which of the followingis a factor of (2+1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1) options(1)2^4-4 (2)2^4-1 (3)2^8+8 (4)2^2+2

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(2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)

\frac{(2 + 1) (2^{2} + 1) (2^{4} + 1) (2^{8} + 1)}{(2^{8} - 1)} = 4^{n} + 1,

n

A = (2 + 1) (2^{2} + 1) (2^{4} + 1) . . . . . (2^{2016} + 1)

{(A + 1)}^{\frac{1}{2016}}

{cot}^{- 1} (2^{2} + \frac{1}{2}) + {cot}^{- 1} (2^{3} + \frac{1}{2^{2}}) + {cot}^{- 1} (2^{4} + \frac{1}{2^{3}}) + . . . . . . \infty

1 = \frac{1}{2} \{1 \times (1 + 1)\} 1 + 2 = \frac{1}{2} \{2 \times (2 + 1)\} 1 + 2 + 3 = \frac{1}{2} \{3 \times (3 + 1)\} 1 + 2 + 3 + 4 = \frac{1}{2} \{4 \times (4 + 1)\}

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