Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the multiplicative order of the roots of $bX^{q^r+1}-aX^{q^r}+dX-c$   In this paper, we find a lower bound for the order of the group $\langle
\theta+\alpha\rangle \subset \overline{\mathbb F_{q}}^*$, where $\alpha\in
\mathbb F_{q}$, $\theta$ is a generic root of the polynomial
$F_{A,r}(X)=bX^{q^r+1}-aX^{q^r}+dX-c\in \mathbb F_{q}[X]$ and $ad-bc\ne0$.

13
The categories of this paper are: quant-ph
3
The categories of this paper are: physics
29
The categories of this paper are: funct-an
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
5
The categories of this paper are: gr-qc
27
The categories of this paper are: comp-gas
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
19
The categories of this paper are: eess
16
The categories of this paper are: stat
28
The categories of this paper are: alg-geom
36
The categories of this paper are: cmp-lg