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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?

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? Correct Answer (2<sup>96</sup> + 1)

Let 232 = x.
Then,
(232 + 1) = (x + 1)
Let (x + 1) be completely divisible by the natural number N.
Then,
(296 + 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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