It is being given that \((2^{32} + 1)\) is completely divisible by a whole number. Which of the following numbers is completely divisible by this number?

**Answer: **D

Let \(2^{32} = x\).

Then, \((2^{32} + 1) = (x + 1)\).

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

\((2^{96} + 1) \\= [(2^{32})^{3} + 1]\\= (x^{3} + 1)\\= (x + 1)(x^{2} - x + 1)\)

which is completely divisible by N, since \((x + 1)\) is divisible by N.

No comment is present. Be the first to comment.

Loading…