deletions | additions       diff --git a/friends.tex b/friends.tex  index 570c94b..d57cede 100644  --- a/friends.tex  +++ b/friends.tex 
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\[  \phi(m)=\vert \{a\in \ZZ_m \mbox{ and a is invertible}\}\vert.  \]  Hence $\phi(7)=6$ and $\phi(12)=4$. In general if $m$ is a prime number $\phi(m)=m-1$. But it is hard for a give number $m$  to compute the Euler function. $\phi(m)$.