Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the generalized Fermat equation $a^2+3b^6=c^n$   In this paper, we prove that the only primitive solutions of the equation
$a^2+3b^6=c^n$ for $n\geq 3$ are $(a,b,c,n)=(\pm 47,\pm 2,\pm 7,4)$. Our proof
is based on the modularity of Galois representations of $\mathbb Q$-curves and
the work of Ellenberg for big values of $n$ and a variety of techniques for
small $n$.

1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
19
The categories of this paper are: eess
33
The categories of this paper are: plasm-ph
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
25
The categories of this paper are: patt-sol
35
The categories of this paper are: mtrl-th
11
The categories of this paper are: hep-lat