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.
\((112 \times 5^{4}) = ?\)
Answer: B
\((112 \times 5^{4})\\= 112 \times \left ( 10\div 2 \right )^{4}\\= \dfrac{112\times 10^{4}}{2^{4}}\\= \dfrac{1120000}{16}\\ = 70000\)
Which one of the following is not a prime number?
Answer: D
91 is divisible by 7. So, it is not a prime number.