cat 2020 Question 26

Question

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

Accepted Answer

ab = $4^{2017} = 2^{4034}$

The total number of factors = 4035.

out of these 4035 factors, we can choose two numbers a,b such that a

And since the given number is a perfect square we have one set of two equal factors.

.'. many pairs(a, b) of positive integers are there such that a≤b and ab=$4^{2017}$ = 2018.

Question 26.