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Question

It is being given that (232 + 1) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?


Options:
A .  `(2^16 + 1)`
B .  `(2^16 - 1)`
C .  `(7 x 2 ^23)`
D .  `(2^96 + 1)`
Answer: Option D

Let 232 = x. Then, (232 + 1) = (x + 1).


Let (x + 1) be completely divisible by the natural number N. Then,


(296 + 1) = [(232)3 + 1] = (x3 + 1) = (x + 1)(x2 - x + 1), which is completely divisible by N, since (x + 1) is divisible by N.




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