Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Small systems of Diophantine equations which have only very large
  integer solutions   Let E_n={x_i=1, x_i+x_j=x_k, x_i \cdot x_j=x_k: i,j,k \in {1,...,n}}. There
is an algorithm that for every computable function f:N->N returns a positive
integer m(f), for which a second algorithm accepts on the input f and any
integer n>=m(f), and returns a system S \subseteq E_n such that S has
infinitely many integer solutions and each integer tuple (x_1,...,x_n) that
solves S satisfies x_1=f(n). For each integer n>=12 we construct a system S
\subseteq E_n such that S has infinitely many integer solutions and they all
belong to Z^n\[-2^{2^{n-1}},2^{2^{n-1}}]^n.

5
The categories of this paper are: gr-qc
22
The categories of this paper are: chao-dyn
29
The categories of this paper are: funct-an
37
The categories of this paper are: supr-con
28
The categories of this paper are: alg-geom
23
The categories of this paper are: solv-int
7
The categories of this paper are: hep-th
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
32
The categories of this paper are: atom-ph
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
27
The categories of this paper are: comp-gas
18
The categories of this paper are: econ
9
The categories of this paper are: nlin
21
The categories of this paper are: adap-org