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For a positive integer $n$ , $\phi(n)$ denotes the number of positive integers less than or equal to $n$ that are relatively prime to $n$ . What is $\phi(2^{100})$ ?

Guest Oct 14, 2018

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$\text{The odd numbers will be relatively prime to }2^{100} \\ \text{so }\phi(2^{100}) = \dfrac 1 2 2^{100} = 2^{99}$

Rom Oct 14, 2018

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Rom · Answer 1 · 2018-10-14T05:20:23

$\text{The odd numbers will be relatively prime to }2^{100} \\ \text{so }\phi(2^{100}) = \dfrac 1 2 2^{100} = 2^{99}$

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