Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Hermite-Joubert problem and a conjecture of Brassil-Reichstein   We show that Hermite theorem fails for every integer $n$ of the form
$3^{k_1}+3^{k_2}+3^{k_3}$ with integers $k_1>k_2>k_3\geq 0$. This confirms a
conjecture of Brassil and Reichstein. We also obtain new results for the
relative Hermite-Joubert problem over a finitely generated field of
characteristic $0$.

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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: physics
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: eess
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: q-alg
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-ph