The correct option is B 172^16 1 =(2^8)^2 1 =(2^8+1) (2^8 1) = (256+1)(256 1) = 257 × 255 =65535 which is exactly divisible by 17. ...

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Remainder Theorem

216-1 divisib...

Question

$2^{16} - 1$ divisible by

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Solution

The correct option is C 17
$2^{16} - 1 = (2^{8})^{2} - 1$
$= (2^{8} + 1) (2^{8} - 1)$
= (256+1)(256-1)
= $257 \times 255 = 65535$ which is exactly divisible by 17.

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