CAT 2020 Exam Shift 3 Solved Paper

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Question : 69 of 76

Marks: +1, -0

How many pairs

( {a}, {b})

of positive integers are there such that

a ≤ b

and

a b=4^{2017}

?

2017
2019
2020
2018

Solution:

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=\;{4034+1+1}/{2}=2018

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