Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the equation $ \boldsymbol{n_1n_2=n_3n_4}$ restricted to factor
  closed sets   We study the number of solutions $N(B,F)$ of the diophantine equation
$n_1n_2=n_3n_4$, where $1\le n_1\le B$, $1\le n_3\le B$, $n_2, n_4\in F$ and
$F\subset [1,B]$ is a factor closed set. We study more particularly the case
when $F= \big\{m=p_1^{\e_1}\ldots p_k^{\e_k}, \e_j\in \{0,1\}, 1\le j\le
k\big\}$,
  $p_1,\ldots,p_k$ being distinct prime numbers.

6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
13
The categories of this paper are: quant-ph
19
The categories of this paper are: eess
34
The categories of this paper are: chem-ph
10
The categories of this paper are: q-bio
29
The categories of this paper are: funct-an
36
The categories of this paper are: cmp-lg
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
16
The categories of this paper are: stat