This question already has an answer here:
While reading about Euler's totient function, I came across this question:
Prove that for a fixed $n$, the equation $\phi (x)=n$ has only a finite number of solutions.
I have thought a lot about it but could not arrive at a proof. I know that $\phi(m_1m_2)=\phi(m_1)\phi(m_2)$ (for $m_1,m_2$ co-prime), but it doesn't seem to help. Any hints/ideas on how to tackle this problem?
Note: I dont think this is a duplicate of Euler Totient Issues, as that question doesn't prove the result. It just clarifies the OP's misinterpretation of another result.