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

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

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Answer:

${2}^{16} - 1$