Q1: 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?

ANS:D - (2⁹⁶ + 1)

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.