Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Solutions of diophantine equations as periodic points of $p$-adic
  algebraic functions, II: The Rogers-Ramanujan continued fraction   In this part we show that the diophantine equation
$X^5+Y^5=\varepsilon^5(1-X^5Y^5)$, where $\varepsilon=\frac{-1+\sqrt{5}}{2}$,
has solutions in specific abelian extensions of quadratic fields
$K=\mathbb{Q}(\sqrt{-d})$ in which $-d \equiv \pm 1$ (mod $5$). The coordinates
of these solutions are values of the Rogers-Ramanujan continued fraction
$r(\tau)$, and are shown to be periodic points of an algebraic function.

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The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
26
The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
17
The categories of this paper are: q-fin
4
The categories of this paper are: cond-mat
16
The categories of this paper are: stat
8
The categories of this paper are: hep-ex
25
The categories of this paper are: patt-sol
21
The categories of this paper are: adap-org
37
The categories of this paper are: supr-con
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
11
The categories of this paper are: hep-lat