Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rational Periodic Points of $x^d+c$ and Fermat-Catalan Equations   We study rational periodic points of polynomial $f_{d,c}(x)=x^d+c$ over the
field of rational numbers, where $d$ is an integer greater than 2. For period
2, we classify all possible periodic points for degrees $d=4,6$. We also
demonstrate the nonexistence of rational periodic points of exact period 2 for
$d=2k$ such that $3\mid 2k-1$ and $k$ has a prime factor greater than 3.
Moreover, assuming the $abc$-conjecture, we prove that $f_{d,c}$ has no
rational periodic point of exact period greater than 1 for sufficiently large
integer $d$ and $c\neq -1$.

15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
33
The categories of this paper are: plasm-ph
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
13
The categories of this paper are: quant-ph
37
The categories of this paper are: supr-con
18
The categories of this paper are: econ
29
The categories of this paper are: funct-an
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
36
The categories of this paper are: cmp-lg
11
The categories of this paper are: hep-lat