Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some Diophantine equations related to positive-rank elliptic curves   We give conditions on the rational numbers a,b,c which imply that there are
infinitely many triples (x,y,z) of rational numbers such that x+y+z=a+b+c and
xyz=abc. We do the same for the equations x+y+z=a+b+c and
x^3+y^3+z^3=a^3+b^3+c^3. These results rely on exhibiting families of
positive-rank elliptic curves.

16
The categories of this paper are: stat
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
28
The categories of this paper are: alg-geom
9
The categories of this paper are: nlin
15
The categories of this paper are: nucl-ex
19
The categories of this paper are: eess
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
10
The categories of this paper are: q-bio
24
The categories of this paper are: dg-ga
22
The categories of this paper are: chao-dyn