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)

E. None of these

Answer: Option D

Solution(By Examveda Team)

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.