Question

2^16 -1 divisible by......17full process shortcut

Answer 1

Answer:

${2}^{16} - 1$

can be expressed as

$( {2}^{8} - 1) \times (2^{8} + 1)$

As

${x}^{2} - {y}^{2} = (x + y) \times (x - y)$

So we can now express

${2}^{8} - 1 = ( {2}^{4} + 1) \times ( {2}^{4} - 1)$

We know that 2^4 +1 is equal to 17 So we can write

${2}^{16} - 1 = ( {2}^{8} - 1) \times 17 \times ( {2}^{4 } - 1)$

Hence it is divisible by 17. Hope it helps you. Mark me as Brainliest if you think I am worth of it.