Math, asked by r0ckYnAv123, 1 year ago

2^16 - 1 is divisible by

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Answered by divya271004

2×2×2×2×2×2×2×2×2×2×2×2×2×2×2×2-1=65536-1
it is divisible by 3
hope it helps...
please mark me as brainiest answer

r0ckYnAv123: Yaa,,it helps but I know it,,its simple understood way

r0ckYnAv123: I want a short trick

r0ckYnAv123: What if in its place there was 2 power 31 or any else longer digit

r0ckYnAv123: Also the options are 11,13,17 and 19

r0ckYnAv123: Then wht

siddhartharao77: the answer is 17

varunankam19: if (a^n - b^n) and n is even then it divides by (a-b) and (a-b)

Answered by siddhartharao77

Given : 2^16 - 1.

Now,

(2^16) - 1

= > (2^8)^2 - 1

= > (2^8)^2 - (1)^2

We know that a^2 - b^2 = (a + b)(a - b).

= > (2^8 + 1)(2^8 - 1)

= > (256 + 1)(256 - 1)

= > (257)(255)

= > 65535.

The obtained number is exactly divisible by 17.

Therefore, 2^16 - 1 is divisible by 17.

Hope this helps!

siddhartharao77: :-)

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