Is 2 power 256 divisible by 17?
Is 2 power 256 divisible by 17?

1Comment
Pritam Prasun @pritam
14 Jan 2020 02:59 am

24 = 16 

Note that 16 is one less than 17.
25 = 32  [ 32 + 2 is divisible ]
26 = 64  [ 64 + 4 is divisible ]
27 = 128 [ 128 + 23 is divisible]
28 = 256 [ 256 + 24  is divisible]
29  =>  29 +  2 is divisible by 17
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2n =>  2n + 2n-4

So,  2256 will be divisible by 17 iff  n + (n - 4) = 256 has integer solution

n + (n - 4) = 256
=> 2n = 260
=> n = 130

Hence, 2256 is divisible by 17

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