CAT 2020 Quant Question [Slot 3] with Solution 19

Question

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

  1. 2017
  2. 2019
  3. 2020
  4. 2018
Option: 4
Solution:

Given, \(a \cdot b = {4^{2017}} = {2^{4034}}\)

Since \(a \cdot b = {4^{2017}},\) is a perfect square the number of factors of \({2^{4034}}\) is odd.

Required answer, the number of values of \(A = \) \(\frac{{4034 + 1 + 1}}{2} = 2018\)

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