Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Counting terms $U_n$ of third order linear recurrences with
  $U_n=u^2+nv^2$   Given a recurrent sequence ${\bf U}:=\{U_n\}_{n\ge 0}$ we consider the
problem of counting ${\mathcal M}_U(x)$, the number of integers $n\le x$ such
that $U_n=u^2+nv^2$ for some integers $u,v$. We will show that ${\mathcal
M}_U(x)\ll x(\log x)^{-0.05}$ for a large class of ternary sequences. Our
method uses many ingredients from the proof of Alba Gonz\'alez and the second
author that ${\mathcal M}_F(x)\ll x(\log x)^{-0.06}$, with $\bf F$ the
Fibonacci sequence.

26
The categories of this paper are: bayes-an
13
The categories of this paper are: quant-ph
32
The categories of this paper are: atom-ph
27
The categories of this paper are: comp-gas
33
The categories of this paper are: plasm-ph
23
The categories of this paper are: solv-int
9
The categories of this paper are: nlin
24
The categories of this paper are: dg-ga
25
The categories of this paper are: patt-sol
16
The categories of this paper are: stat
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The categories of this paper are: q-alg
12
The categories of this paper are: nucl-th
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The categories of this paper are: mtrl-th
28
The categories of this paper are: alg-geom
34
The categories of this paper are: chem-ph
6
The categories of this paper are: astro-ph