{
  "abstract": "For a finite multiset of integers, repeatedly choose two entries $a,b$ and replace them with $|a^{2}-b^{2}|$. Hickerson and Kleber asked whether, for every integer $n$, the set ${n,n+1,\\ldots,n+35}$ can be reduced to zero. We give an explicit reduction. Together with their results for lengths 12 and 24, this gives, for every positive integer $L$, [ {n,n+1,\\ldots,n+L-1}\\text{ reduces to zero for every }n\\in\\mathbb Z \\Longleftrightarrow 12\\mid L\\text{ and }L\\ge 24. ]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.00098",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhao Shen"
    },
    {
      "name": "Youran Wu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0mhtgssjgcdjj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.00098",
  "fulltext_url": null,
  "id": "0mhtgssjgcdjj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.00098",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "openalex",
      "2607|Advanced Combinatorial Mathematics"
    ]
  ],
  "openalex": "W7206202919",
  "pdf_url": "https://arxiv.org/pdf/2609.00098",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0mhtgssjgcdjj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:04Z",
      "native_id": "2609.00098",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.00098"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    }
  ],
  "title": "Reducing Every Set of 36 Consecutive Integers to Zero by Differences of Squares",
  "title_text": "Reducing Every Set of 36 Consecutive Integers to Zero by Differences of Squares",
  "type": "preprint",
  "updated_at": "2026-10-30T12:18:04Z",
  "url": "https://research.draconitic.com/paper/0mhtgssjgcdjj",
  "venue": "arXiv",
  "versions": []
}