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al-mahed
#4
Feb8-11, 06:45 PM
P: 258
Inverse image of phi (totient)

Quote Quote by math_grl View Post
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 math-grl

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