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How do I generalize the equation to be able to plug in any result for $\phi(n)=12$ and find any possible integer that works?

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    Welcome to math.SE! It would be useful to provide some more context for your problem (for example, the definition of $\mu$, which I simply assume denotes the Mobius function here). We have guidelines for asking good questions (which usually mean good answers!) in the [faq](http://math.stackexchange.com/faq), which I suggest you take a look at.2012-01-23
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    I am guessing when you write $\mu$ you mean something other then the Mobius function? Perhaps you are asking for which $n$, $\phi(n)=12$ (the totient function) It we be good to clarify, since $\mu(n)$ can only take the values $-1,0,1$. (ie, not $12$)2012-01-23
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    I've taken the liberty of changing $\mu$ to $\phi$ since it seems that's what's intended.2012-01-23

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