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.

Hence, option 4 is the correct answer.