Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A group-theoretical approach to Lehmer's totient problem   Lehmer's totient problem asks whether there exists any composite number $n$
such that $\varphi(n) \, \mid \, (n-1)$, where $\varphi$ is Euler totient
function. It is known that if any such $n$ exists, it must be Carmichael and $n
> 10^{30}$. In this paper, we develop a new approach to the problem via some
recent results in group theory related to a function $\psi$ (the sum of order
of elements of a group) and show that if $k \varphi(n) = n-1$ for some integer
$k$, then $k$ must be $\geq 3$, and actually, if $5, 7, 11, 13 \not | n$, $k
\geq 4$. This implies that any counterexample must be such that $n > 10^{8171}$
and $\omega(n) \geq 1991$.

8
The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
17
The categories of this paper are: q-fin
12
The categories of this paper are: nucl-th
26
The categories of this paper are: bayes-an
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
28
The categories of this paper are: alg-geom