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Erdős problem / erdos

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Problem 727

Exact records and bounded producer offers matched to this problem.

Current bounded offer

rank 10
availableerdos:727
Erdős 727
Advance Erdős problem 727 from its pinned statement, theorem and proof records, attempts, residual obligations, dependency context, and source locks; produce one decision-relevant artifact or an informative negative result without repeating banked routes.
  1. Targeterdos:727
  2. Packetsite/problems/727.json
  3. Verifiererdos-frontier.problem-work.v1
Inspect ranked work
Exact offer contractPacket, root, and verifier profile
Verifier
erdos-frontier.problem-work.v1
Packet
site/problems/727.json
Packet root
sha256:e33b6172266741c377a93b68f26a35afc6a1aff7b9a8990541fde4bd37e843af

Matching finding records

1 records

  1. vf_6a47d7e08d31041a

    theoretical

    Erdős Problem #727: declared status 'open'. Formalized: yes. Let k≥2k\geq 2. Does(n+k)!2∣(2n)!(n+k)!^2 \mid (2n)!for infinitely many nn? Current best: Erd\H{o}s [Er68c] proved that if a!b!∣n!a!b!\mid n! then a+b≤n+O(log⁡n)a+b\leq n+O(\log n). Prize: no. OEIS: A002503, A343507, A389396. Tags: factorials, number theory.

    recordedOpen record