Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sums of two ${s}$-units via frey-hellegouarch curves   In this paper, we develop a new method for finding all perfect powers which
can be expressed as the sum of two rational S-units, where S is a finite set of
primes. Our approach is based upon the modularity of Galois representations
and, for the most part, does not require lower bounds for linear forms in
logarithms. Its main virtue is that it enables to carry out such a program
explicitly, at least for certain small sets of primes S; we do so for S = {2,
3} and S = {3, 5, 7}.

33
The categories of this paper are: plasm-ph
0
The categories of this paper are: hep-ph
10
The categories of this paper are: q-bio
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
19
The categories of this paper are: eess
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
36
The categories of this paper are: cmp-lg
15
The categories of this paper are: nucl-ex