(I didn't find any other posts related to this but I think this is a weird because my question seems like a very natural one.)
Let $\varphi$ denote the Euler Totient Function. Given $m$ an even number, can we find all the positive integers $n$ such that $\varphi(n)=m$? If not, at least can we tell how many there are? Are there infinite? Why?
I strongly believe this is a hard task.
Thank you in advance.
Finite. $$ \varphi(n) \geq \sqrt {\frac{n}{2}} $$
More complete statements and a proof as two answers at Is the Euler phi function bounded below?