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CAT 2020 Question Paper (Slot 3) Question 70
Question 70

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

Solution

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

The total number of factors = 4035.

out of these 4035 factors, we can choose two numbers a,b such that a<b in [4035/2] = 2017.

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 $$a\leq b$$ and $$ab=4^{2017}$$ = 2018. 


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