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Erdős problem 321

What is the largest A{1,,N}A\subseteq\{1,\dots,N\} such that all subset sums nS1/n\sum_{n\in S}1/n (over SAS\subseteq A) are distinct?
Retained from Erdős Problems · not edited here
Formal statements
4 open · 2 solved
Erdős Problems says
solved
Decision here
accepted
Checks
1 check · 6 formal

A two-sided asymptotic bound on extremalSize

Still unresolved: At Formal Conjectures commit 59f30aa314ba225fcd9268723ce8291616df1ab0, the Lean development starfleet/erdos-321 establishes a two-sided asymptotic bound on extremalSize, which denotes the same quantity as Formal Conjectures' Erdos321.R and therefore supplies a candidate answer for the exact occurrence Erdos321.erdos_321.variants.isTheta, not a proof of it.

Exact result and limitations

At Formal Conjectures commit 59f30aa314ba225fcd9268723ce8291616df1ab0, the Lean development starfleet/erdos-321 establishes a two-sided asymptotic bound on extremalSize, which denotes the same quantity as Formal Conjectures' Erdos321.R and therefore supplies a candidate answer for the exact occurrence Erdos321.erdos_321.variants.isTheta, not a proof of it. For occurrence resolution only, the exact occurrences Erdos321.erdos_321 and Erdos321.erdos_321.variants.isTheta are associated with problem:erdos:321 under resolver root sha256:a9d6787719c5c8069a9e14ade0f5a62975410272e6cd1583865b282d1d8669dd. At the exact retained Erdős 321 source revisions, the terminal theorem and structural comparison do not establish implication to either fixed Nat.log variant.

  • Exact source revisions, occurrence resolver root, and retained evidence/current/erdos-321 inputs only.
  • Caveat: Erdos problem 321 remains open; this does not assert resolution or optimality.
  • Caveat: Occurrence association is navigation-only and establishes no statement equivalence.
  • Caveat: The negative comparison does not show that a bridge is impossible or that either statement is false.
  • Caveat: The retained terminal and fixed sources have no exact resolved joint Lean environment.
Type
theoretical
Evidence
1 artifact
Decision
accepted
Reviewed
Aug 17, 2026, 6:33 PM

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