Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Explicit rational solutions to the Variants of Erd\H{o}s- Selfridge
  superelliptic curves   For the superelliptic curves of the form $$ (x+1) \cdots(x+i-1)(x+i+1)\cdots
(x+k)=y^\ell$$ with $x,y \in \mathbb{Q}$, $y\neq 0$, $k \geq 3$, $1\leq i\leq
k$, $\ell \geq 2,$ a prime. Das, Laishram, Saradha[2018] and Edis[2019] showed
that the superelliptic curve has no rational points for $\ell\geq e^{3^k}$. In
fact, the double exponential bound, obtained in these papers is far from
reality. In this paper, we study the superelliptic curves for small values of
$k$. In particular, we explicitly solve the above equation completely for $4
\leq k \leq 8.$

7
The categories of this paper are: hep-th
0
The categories of this paper are: hep-ph
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
31
The categories of this paper are: ao-sci
12
The categories of this paper are: nucl-th
22
The categories of this paper are: chao-dyn
32
The categories of this paper are: atom-ph
18
The categories of this paper are: econ
21
The categories of this paper are: adap-org
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
25
The categories of this paper are: patt-sol
1
The categories of this paper are: cs
20
The categories of this paper are: acc-phys
14
The categories of this paper are: math-ph