Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Perfect numbers and Fibonacci primes   In this paper, we introduce the concept of $F$-perfect number, which is a
positive integer $n$ such that $\sum_{d|n,d<n}d^2=3n$. We prove that all the
$F$-perfect numbers are of the form $n=F_{2k-1}F_{2k+1}$, where both $F_{2k-1}$
and $F_{2k+1}$ are Fibonacci primes. Moreover, we obtain other interesting
results and raise a new conjecture on perfect numbers.

3
The categories of this paper are: physics
1
The categories of this paper are: cs
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
27
The categories of this paper are: comp-gas
10
The categories of this paper are: q-bio
0
The categories of this paper are: hep-ph
18
The categories of this paper are: econ
37
The categories of this paper are: supr-con
19
The categories of this paper are: eess
35
The categories of this paper are: mtrl-th
20
The categories of this paper are: acc-phys
23
The categories of this paper are: solv-int
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg