Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Lehmer's problem involving Euler's totient function   The Euler's totient function $ \varphi(n) $ counts the positive integers up
to a given integer $ n$ that are relatively prime to $ n $. We solve a problem
due to Lehmer that there is no composite number $ n $ such that $
\varphi(n)\mid n-1 $. We also note that there are infinitely many primes that
are not Sophie Germain primes.

26
The categories of this paper are: bayes-an
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
3
The categories of this paper are: physics
33
The categories of this paper are: plasm-ph
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
18
The categories of this paper are: econ
13
The categories of this paper are: quant-ph
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol