Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Twists of X(7) and primitive solutions to x^2+y^3=z^7   We find the primitive integer solutions to x^2+y^3=z^7. A nonabelian descent
argument involving the simple group of order 168 reduces the problem to the
determination of the set of rational points on a finite set of twists of the
Klein quartic curve X. To restrict the set of relevant twists, we exploit the
isomorphism between X and the modular curve X(7), and use modularity of
elliptic curves and level lowering. This leaves 10 genus-3 curves, whose
rational points are found by a combination of methods.

20
The categories of this paper are: acc-phys
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
8
The categories of this paper are: hep-ex
13
The categories of this paper are: quant-ph
27
The categories of this paper are: comp-gas
19
The categories of this paper are: eess
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th