Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A modular approach to the generalized Ramanujan-Nagell equation   Let $k$ be a positive integer. In this paper, using the modular approach, we
prove that if $k\equiv 0 \pmod{4}$, $30< k<724$ and $2k-1$ is an odd prime
power, then under the GRH, the equation $x^2+(2k-1)^y=k^z$ has only one
positive integer solution $(x,y,z)=(k-1,1,2)$. The above results solve some
difficult cases of Terai's conecture concerning this equation.

30
The categories of this paper are: q-alg
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
14
The categories of this paper are: math-ph
15
The categories of this paper are: nucl-ex
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph
20
The categories of this paper are: acc-phys
13
The categories of this paper are: quant-ph
0
The categories of this paper are: hep-ph
26
The categories of this paper are: bayes-an