{
  "abstract": "We give a new proof of the fact that every 2-coloring of the positive integers contains a monochromatic Pythagorean triple. This result was originally proven by Heule, Kullmann, and Marek with SAT solvers in 2016, answering a decades-old question of Graham. This proof uses elementary techniques and requires neither lengthy computation nor difficult analytic machinery.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.39063",
  "author_total": 1,
  "authors": [
    {
      "name": "William J. Wesley"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/82xb7bjrnfhyp.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.39063",
  "fulltext_url": null,
  "id": "82xb7bjrnfhyp",
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  "landing_url": "https://arxiv.org/abs/2609.39063",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
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      "arxiv",
      "math.CO"
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      "2607|Limits and Structures in Graph Theory"
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  "openalex": "W7215028877",
  "pdf_url": "https://arxiv.org/pdf/2609.39063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-30",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/82xb7bjrnfhyp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:49Z",
      "native_id": "2609.39063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.39063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "An elementary proof of the 2-regularity of Pythagorean triples",
  "title_text": "An elementary proof of the 2-regularity of Pythagorean triples",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:49Z",
  "url": "https://research.draconitic.com/paper/82xb7bjrnfhyp",
  "venue": "arXiv",
  "versions": []
}