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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 .  (216 + 1)
B .  (216 - 1)
C .  (7 x 223)
D .  (296 + 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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