Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The investigation of Euler's totient function preimages   We propose a lower estimation for computing quantity of the inverses of
Euler's function. We answer the question about the multiplicity of $m$ in the
equation $\varphi(x) = m$ \cite{Ford}. An analytic expression for exact
multiplicity of $m = {{2}^{{{2}^{n}}+a}}$, where $a\in N$, $a<{{2}^{n}}$,
$\varphi(t)={{2}^{{{2}^{n}}+a}}$ was obtained. A lower bound of inverses number
for arbitrary $m$ was found. New numerical metric was proposed.

24
The categories of this paper are: dg-ga
5
The categories of this paper are: gr-qc
13
The categories of this paper are: quant-ph
22
The categories of this paper are: chao-dyn
28
The categories of this paper are: alg-geom
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
37
The categories of this paper are: supr-con
3
The categories of this paper are: physics
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
34
The categories of this paper are: chem-ph
9
The categories of this paper are: nlin