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Erdős problem #728: factorial divisibility

How large can a+b−n be when a!b!

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Understanding the problem

Read the background

How large can a+b−n be when a!b! divides n!(a+b−n)!, with a and b restricted to a middle range relative to n? The restrictions exclude trivial constructions.

This guide separates the original research claim from the status of any supporting formal artifact. Compare statements before comparing evidence badges.

Why it matters

A concrete target that separates mathematical novelty, formalization, and evidence.

What counts as progress

A new precisely scoped theorem, construction, bound, or documented formalization, compared with the relevant baseline.

What to watch for

  • Read the exact theorem and restrictions in the original source.
  • Separate a result’s discovery from its formalization and later independent checking.
  • Retain prior work, revisions, and the contribution of human researchers.

Background review: 2026-10-11. Selected sources:

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