Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On some general solutions of the simple Pell equation   Two theorems are demonstrated giving analytical expressions of the
fundamental solutions of the Pell equation $X^{2}-DY^{2}=1$ found by the method
of continued fractions for two squarefree polynomial expressions of radicands
of Richaud-Degert type $D$ of the form
$D=\left(f\left(u\right)\right)^{2}\pm2^{\alpha}n$, where $D$, $n>0$,
$\alpha\geq0,\in\mathbb{Z}$, and $f\left(u\right)>0,\in\mathbb{Z}$, any
polynomial function of $u\in\mathbb{Z}$ such that
$f\left(u\right)\equiv0\left(mod\,\left(2^{\alpha-1}n\right)\right)$ or
$f\left(u\right)\equiv\left(2^{\alpha-2}n\right)\left(mod\,\left(2^{\alpha-1}n\right)\right)$.

25
The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
4
The categories of this paper are: cond-mat
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
24
The categories of this paper are: dg-ga
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
14
The categories of this paper are: math-ph
3
The categories of this paper are: physics
17
The categories of this paper are: q-fin
7
The categories of this paper are: hep-th
11
The categories of this paper are: hep-lat
18
The categories of this paper are: econ