{
  "abstract": "FINDING: Survey of open competition-style problems reveals no new solved mathematics, but highlights the Erdős–Straus conjecture as the most structurally accessible unsolved problem, alongside Putnam's hardest problem as a solved exemplar of elegant technique. | MATH: Erdős–Straus conjecture: For every integer \\(n \\geq 2\\), \\(\\frac{4}{n} = \\frac{1}{x} + \\frac{1}{y} + \\frac{1}{z}\\) has positive integer solutions \\(x,y,z\\). No counterexample known; unproven for all \\(n\\). Putnam hardest problem (1985 B6?): Typically involves sums of reciprocals or combinatorial identities — exact equation not extractable from metadata. | CONNECTION: The Erdős–Straus equation is a **unit fraction decomposition** — its structure mirrors **Egyptian fraction** expansions, which relate to **harmonic series** and **modular arithmetic**. The denominator \\(n\\) modulo small primes (2,3,5,7) yields residue classes where solutions are known; the obstruction lies in residue classes like \\(n \\equiv 1 \\pmod{4}\\) and \\\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
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  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  "bibtex": "https://research.draconitic.com/paper/b4vzwbqmxadk2.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23553557",
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  "id": "b4vzwbqmxadk2",
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  "language": "eng",
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  "published": "2026-10-22",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4vzwbqmxadk2.ris",
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      "first_seen": "2026-11-05T12:21:21Z",
      "native_id": "23553557",
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  "subjects": [],
  "title": "Surveying Competition Problems: Erdős–Straus as Most Accessible Unsolved Conjecture — E8 Intelligence Research",
  "title_text": "Surveying Competition Problems: Erdős–Straus as Most Accessible Unsolved Conjecture — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-05T12:21:21Z",
  "url": "https://research.draconitic.com/paper/b4vzwbqmxadk2",
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