Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Integers of the Form $ax^2+bxy+cy^2$   We provide a characterization of integers represented by the positive
definite binary quadratic form $ax^2+bxy+cy^2$. In order to prove the main
theorem, we define the "relative conductor" of two orders in an imaginary
quadratic field. Then we provide a characterization of decomposition of proper
ideals of orders in imaginary quadratic fields. Moreover we present some
interesting examples of the main theorem.

15
The categories of this paper are: nucl-ex
29
The categories of this paper are: funct-an
30
The categories of this paper are: q-alg
3
The categories of this paper are: physics
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The categories of this paper are: stat
25
The categories of this paper are: patt-sol
13
The categories of this paper are: quant-ph
1
The categories of this paper are: cs
18
The categories of this paper are: econ
31
The categories of this paper are: ao-sci
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The categories of this paper are: dg-ga
20
The categories of this paper are: acc-phys
36
The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
35
The categories of this paper are: mtrl-th
19
The categories of this paper are: eess