Up to my knowledge, this problem is open (see http://mathworld.wolfram.com/CarmichaelsTotientFunctionConjecture.html ).

That is strange... Hojoo, do you have the book in which this appears, or could you check it with the person that contributed this?

Peter wrote: Show that if the equation $\phi(x)=n$ has one solution, it always has a second solution, $n$ being given and $x$ being the unknown. I'm not sure... but it seems that I also included some open problems

I have asked this problem on ML.Actually,I have tried to solve this one for a day.so disppointed.I think I have no ability to solve an open problem...