Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-linear Recurrences that Quite Unexpectedly Generate Rational Numbers   Non-linear recurrences which generate integers in a surprising way have been
studied by many people. Typically people study recurrences that are linear in
the highest order term. In this paper I consider what happens when the
recurrence is not linear in the highest order term. In this case we no longer
produce a unique sequence, but we sometimes have surprising results. If the
highest order term is raised to the $m^{th}$ power we expect answers to have
$m^{th}$ roots, but for some specific recurrences it happens that we generate
rational numbers ad infinitum. I will give a general example in the case of a
first order recurrence with $m=2$, and a more specific example that is order 3
with $m=2$ which comes from a generalized Somos recurrence.

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The categories of this paper are: funct-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: bayes-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: cs
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: ao-sci
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The categories of this paper are: stat