Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the cubic Pell equation over finite fields   The classical Pell equation can be extended to the cubic case considering the
elements of norm one in $Z[\sqrt[3]{r}]$, which satisfy $x^3 + r y^3 + r^2 z^3
- 3 r x y z = 1$. The solution of the cubic Pell equation is harder than the
classical case, indeed a method for solving it as Diophantine equation is still
missing. In this paper, we study the cubic Pell equation over finite fields,
extending the results that hold for the classical one. In particular, we
provide a novel method for counting the number of solutions in all possible
cases depending on the value of r. Moreover, we are also able to provide a
method for generating all the solutions.

30
The categories of this paper are: q-alg
21
The categories of this paper are: adap-org
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
34
The categories of this paper are: chem-ph
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
23
The categories of this paper are: solv-int
16
The categories of this paper are: stat
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
5
The categories of this paper are: gr-qc