Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Properties of the Digital Root and its Extension to Rational Numbers --
  an Algebraic Approach   This paper contains an algebraic constructive and self-contained account of
the invariance rule of the digital root under division for an arbitrary natural
basis representation. Both the cases of repeating and non-repeating fractionals
are treated. In the preliminary section some known results such as the
uniqueness in the representation of a fraction are discussed for both the
finite and infinite bases cases. Simple examples are introduced throughout the
text for illustrative purposes.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
32
The categories of this paper are: atom-ph
6
The categories of this paper are: astro-ph
22
The categories of this paper are: chao-dyn
37
The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: stat
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The categories of this paper are: econ
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The categories of this paper are: chem-ph
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: cs
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The categories of this paper are: q-bio