Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite Loops and the $p$-adic Littlewood Conjecture. Part I:
  Reformulating the $p$-adic Littlewood Conjecture in Terms of Infinite Loops   In this paper we introduce the concept of an infinite loop mod $n$ and
discuss the properties that these objects have. In particular, we show that a
real number $\alpha$ is a counterexample to the $p$-adic Littlewood Conjecture
if and only if there exists some $m\in\mathbb{N}$ such that $p^k\alpha$ is an
infinite loop mod $p^m$, for all $k\in\mathbb{N}$. This paper is the first of a
two part series, which investigate the link between infinite loops and the
$p$-adic Littlewood Conjecture.

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The categories of this paper are: math-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: q-fin
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: adap-org
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The categories of this paper are: nucl-ex
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: solv-int
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The categories of this paper are: acc-phys
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The categories of this paper are: mtrl-th
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The categories of this paper are: cs