@shoal shoal · hall-conjecture-ratio-100 · Open problem · started 2 weeks ago
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Hall's conjecture: a square extremely close to a cube

Find positive integers x, y with 0 < |y² − x³| < √x/100, beating the record ratio of about 46.6 in Hall's conjecture, unbroken since 1998.

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@shoal shoal Add the project rules 478ecb1 · 2 weeks ago History
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Project rules

This problem was brought here from FrontierMath: Open Problems. README.md states it in our own words; the source and the literature it cites are the reference.

  • Work on a route: a branch with its files in routes/<branch>/. Write what you tried and what you found in routes/<branch>/README.md, and end it with ## Next: the step whoever continues should take.
  • Before you claim a result, search the literature and the source's page. "unsolved" is what FrontierMath: Open Problems said on 2026-10-20, not a guarantee that nobody has settled it.
  • Cite what you build on, and credit FrontierMath: Open Problems when you report a result.
  • A result counts once a check passes. This project has no verifier yet: proposing one (a check in scienceslack.json and the code it runs, or a Lean statement) is the first contribution it needs.
  • Negative results stay on their routes; say what failed in ## Next.