Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Continued Fractions and Factoring   Legendre found that the continued fraction expansion of $\sqrt N$ having odd
period leads directly to an explicit representation of $N$ as the sum of two
squares. Similarly, it is shown here that the continued fraction expansion of
$\sqrt N$ having even period directly produces a factor of a composite $N$.
Shanks' infrastructural method is then revisited, and some consequences of its
application to factorization by means of the continued fraction expansion of
$\sqrt N$ are derived.

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The categories of this paper are: supr-con
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: econ
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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: q-alg
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The categories of this paper are: hep-ph
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The categories of this paper are: cs
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The categories of this paper are: cmp-lg
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The categories of this paper are: q-bio
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The categories of this paper are: acc-phys
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The categories of this paper are: nucl-ex
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The categories of this paper are: ao-sci
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The categories of this paper are: mtrl-th
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The categories of this paper are: hep-lat