Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A Swan-like note for a family of binary pentanomials   In this note, we employ the techniques of Swan (Pacific J. Math. 12(3):
1099-1106, 1962) with the purpose of studying the parity of the number of the
irreducible factors of the penatomial
$X^n+X^{3s}+X^{2s}+X^{s}+1\in\mathbb{F}_2[X]$, where $s$ is even and $n>3s$.
Our results imply that if $n \not\equiv \pm 1 \pmod{8}$, then the polynomial in
question is reducible.

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The categories of this paper are: q-bio
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The categories of this paper are: adap-org
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The categories of this paper are: dg-ga
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The categories of this paper are: econ
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: supr-con
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-th