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?

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?
[A].

(216 + 1)

[B].

(216 – 1)

[C].

(7 x 223)

[D].

(296 + 1)

Answer: Option D

Explanation:

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.