Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational points on certain quintic hypersurfaces   Let $f(x)=x^5+ax^3+bx^2+cx \in \Z[x]$ and consider the hypersurface of degree
five given by the equation \cal{V}_{f}: f(p)+f(q)=f(r)+f(s). Under the
assumption $b\neq 0$ we show that there exists $\Q$-unirational elliptic
surface contained in $\cal{V}_{f}$. If $b=0, a<0$ and $-a\not\equiv 2,18,34
\pmod {48}$ then there exists $\Q$-rational surface contained in $\cal{V}_{f}$.
Moreover, we prove that for each $f$ of degree five there exists
$\Q(i)$-rational surface contained in $\cal{V}_{f}$.

19
The categories of this paper are: eess
1
The categories of this paper are: cs
7
The categories of this paper are: hep-th
31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
30
The categories of this paper are: q-alg
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
17
The categories of this paper are: q-fin
0
The categories of this paper are: hep-ph
29
The categories of this paper are: funct-an
3
The categories of this paper are: physics
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ