Question

How many pairs $(a, b)$ of positive integers are there such that $a≤b$ and $ab=4^{2017}$ ?

• A. 2017
• B. 2019
• C. 2020
• D. 2018

Answer 1

Answer: (D)

2018

Answer 2

The correct answer is (D): $2018$
Given, $a.b = 4^{2017} = 2^{4034}$
Since $a.b$ = $4^{2017}$, is a perfect square the number of factors of $2^{4034}$ is odd.
Required answer, the number of values of $A$ = $\frac{4034+1+1}{2} = 2018$