The question is about Divisibility of higher powers of a number. A term is divisible by x and we need to find out another term which is also divisible by x . Dealing with digits and base system of a number is a vital component in CAT Number Systems. A range of CAT questions can be asked based on this simple concept in the CAT Exam.

Question 9: A number 4^{16} + 1 is divisible by x. Which among the following is also divisible by x?

- 4
^{96}+ 1 - 4
^{32}+ 1 - 4
^{8}+ 1 - 4
^{48}+ 1

4

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We know a^{3} + b^{3} = (a + b)^{3} – 3ab(a + b)

If (a + b) is divisible by x, then a^{3} + b^{3} is also divisible by x.

If 4^{16} + 1 is divisible by x, then (4^{16})^{3} + 1^{3} is also divisible by x

Or 4^{48} + 1 is divisible by x

The question is **"Which among the following is also divisible by x?"**

Choice D is the correct answer.

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