Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Coloring so that no Pythagorean Triple is Monochromatic   We address the question of the "partition regularity" of the Pythagorean
equation a^2+b^2=c^2; in particular, can the natural numbers be assigned a
2-coloring, so that no Pythagorean triple (i.e., a solution to the equation) is
monochromatic? We prove that the hypergraph of Pythagorean triples can contain
no Steiner triple systems, a natural obstruction to 2-colorability. Then, after
transforming the question into one about 3-CNF satisfiability and applying some
reductions, a SAT solver is used to find a 2-coloring for {1,...,7664}. Work
continues as we seek to improve the reductions and extend the computation.

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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: stat
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The categories of this paper are: hep-lat
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The categories of this paper are: solv-int
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The categories of this paper are: chao-dyn
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The categories of this paper are: adap-org
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The categories of this paper are: hep-ex
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: hep-ph
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The categories of this paper are: q-alg