Quote by math_grl
I don't think there should be any confusion in my terminology but in case a refresher is needed check out http://en.wikipedia.org/wiki/Image_%...#Inverse_image
It might also help make it clear that [tex]f: \mathbb{N} \rightarrow \phi(\mathbb{N})[/tex] where [tex]f(n) = \phi(n)[/tex] cannot have an inverse as it's onto but not injective.
Other than that, yes, what I was asking if there was a way to find all those numbers that map to 14 (for example) under phi...

hi mathgrl
so what you want is to find the n's such that
[tex]\varphi(n_1)=m_1[/tex]
[tex]\varphi(n_2)=m_2[/tex]
[tex]\varphi(n_3)=m_3[/tex]
[tex]\varphi(n_4)=m_4[/tex]
...
knowing only the m's, correct?
there is a conjecture related to it, although what you want is far more difficult than the conjecture
http://en.wikipedia.org/wiki/Carmich...ion_conjecture