Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the divisibility of class numbers and discriminants of imaginary
  quadratic fields   Let $n$ be a squarefree positive odd integer. We will show that there exist
infinitely many imaginary quadratic number fields with discriminant divisible
by $n$ and-at the same time-having an element of order $n$ in the class group.
We then apply our result to prove that for a given squarefree positive odd
integer $n$ there exist infinitely many $N$ such that $n$ divides both $N$ and
$r(N)$, where $r(N)$ is the representation number of $N$ as sums of three
squares.

27
The categories of this paper are: comp-gas
8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
3
The categories of this paper are: physics
30
The categories of this paper are: q-alg
15
The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
13
The categories of this paper are: quant-ph
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
24
The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
12
The categories of this paper are: nucl-th
0
The categories of this paper are: hep-ph
17
The categories of this paper are: q-fin
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The categories of this paper are: eess