Erdős problems frontier

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  "text": "Erdős Problem #397 has status 'disproved (lean)'. Statement: Are there only finitely many solutions to $$ \\prod_i \\binom{2m_i}{m_i}=\\prod_j \\binom{2n_j}{n_j} $$ with the $m_i,n_j$ distinct? Somani, using ChatGPT, has given a negative answer. In fact, for any $a\\geq 2$, if $c=8a^2+8a+1$, $\\binom{2a}{a}\\binom{4a+4}{2a+2}\\binom{2c}{c}= \\binom{2a+2}{a+1}\\binom{4a}{2a}\\binom{2c+2}{c+1}.$ Further families of solutions are given in the comments by SharkyKesa. This was earlier asked about in a [MathOverflow] question, in response to which Elkies also gave an alternative construction which produces solutions - at the moment it is not clear whether Elkies' argument gives infinitely many solutions (although Bloom believes that it can). This was formalized in Lean by Wu using Aristotle. Topics: number theory, binomial coefficients. Erdős prize: no. Statement is machine-verified in Lean (formal-conjectures). OEIS: N/A.",
  "type": "open_question"
 },
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  "text": "Agent-imported candidate claim; scope requires review."
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  "extraction_confidence": 0.7,
  "kind": "frontier_epistemic",
  "method": "expert_judgment",
  "score": 0.99
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 "created": "2026-05-30T00:42:06.826507+00:00",
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    "artifact_packet_id": "cap_61973ee16b553d57",
    "candidate_claim_id": "vc_14a414673be11d68"
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 "provenance": {
  "authors": [
   {
    "name": "Erdős Open-Problem spine ingest",
    "orcid": null
   }
  ],
  "citation_count": null,
  "doi": null,
  "extraction": {
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  "source_type": "model_output",
  "title": "cap_61973ee16b553d57 · vc_14a414673be11d68",
  "url": "https://www.erdosproblems.com/397",
  "year": null
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