Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Non-Negative Integer Linear Congruences   We consider the problem of describing all non-negative integer solutions to a
linear congruence in many variables. This question may be reduced to solving
the congruence $x_1 + 2x_2 + 3x_3 + ... + (n-1)x_{n-1} \equiv 0 \pmod n$ where
values of the unknowns, $x_i$, are sought among the non-negative integers. We
consider the monoid of solutions of this equation and prove a conjecture of
Elashvili concerning the structure of these solutions. This yields a simple
algorithm for generating most (conjecturally all) of the high degree
indecomposable solutions of the equation.

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The categories of this paper are: cond-mat
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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: hep-th
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: dg-ga
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-ph
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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph