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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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+1
Best Answer

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

Rom  Oct 14, 2018

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