View Single Post
P: 258
Inverse image of phi (totient)

 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 $$f: \mathbb{N} \rightarrow \phi(\mathbb{N})$$ where $$f(n) = \phi(n)$$ 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

$$\varphi(n_1)=m_1$$
$$\varphi(n_2)=m_2$$
$$\varphi(n_3)=m_3$$
$$\varphi(n_4)=m_4$$
...

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