Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the functional equation Af^2+Bg^2=1 in a p-adic field of
  characteristic zero   For a fixed prime $p$, let $\mathbb C_p$ denote the complex $p$-adic numbers.
For polynomials $A,B\in \mathbb C_p[x]$ we consider decompositions
$A(x)f^2(x)+B(x)g^2(x)=1$ of entire functions $f,\,g$ on $\mathbb C_p$ and try
to improve an impossibility result due to A. Boutabaa concerning transcendental
$f,g$. We also provide an independent proof of a $p$-adic diophantic statement
due to D. N. Clark, which is an important ingredient of Boutabaa's method.

3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
12
The categories of this paper are: nucl-th
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
28
The categories of this paper are: alg-geom
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
30
The categories of this paper are: q-alg