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

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

Accepted Answer

2018. a b = 4 2017 = 2 4034 ab\ =\ 4^{2017}=2^{4034} 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,

How many pairs(a, b) of positive integers are there such that a≤ba\leq ba≤b and ab=42017ab=4^{2017}ab=42017 ?

How many pairs(a, b) of positive integers are there such that a≤ba\leq ba≤b and ab=42017ab=4^{2017}ab=42017 ?

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

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