Exams › IBPS PO › Quantitative Aptitude

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

1. \((2^{16} + 1)\)
2. \((2^{16} - 1)\)
3. \((7 \times 2^{23})\)
4. \((2^{96} + 1)\)

Correct answer: \((2^{96} + 1)\)

Solution

A factor of \(2^{32}+1\) will also divide expressions built from compatible powers using the identity for \(a^{3n}+1\). Among the options, \(2^{96}+1\) matches this pattern because \(96=3\times 32\). Hence it is divisible by the same whole number.

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