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Erdős problem 42

Erdős Problem 42: Let M ≥ 1 and N be sufficiently large in terms of M. Is it true that for every maximal Sidon set A ⊆ {1,…,N} there is another Sidon set B ⊆ {1,…,N} of size M such that (A - A) ∩ (B - B) = {0}?

No current result

No reviewed Result is current in Vela Mathematics Program. Retained source material is shown below.

Retained declaration

FormalConjectures/ErdosProblems/42.lean

Formal Conjectures

FormalConjectures/ErdosProblems/42.leanErdos42.erdos_424 linesExact file
TrueM ≥ 1,    ∀ᶠ (N : ℕ) in Filter.atTop,      ∀ (A : Set ℕ), A.IsMaximalSidonSetIn N → ∃ BSet.Icc 1 N, IsSidon BB.ncard = M ∧ (A - A) ∩ (B - B) = {0}
SolvedProof has a holelean4external proof

The proof uses `sorry`: part of the argument is written but not proved. Lean accepts the file; it does not accept the theorem.

Proof manifests naming this Problem

  • Jayyhk Erdős Leanjayyhk:erdos:42
  • PLBY Lean proofsErdosProblems.Erdos42

Reported activity

Work these sources record against this Problem. Source-reported attribution, not reviewed here.

  • AI standalone

    Erdős AI contributions wiki · 19 Jan, 2026

    Machine
    Codex, GPT-5.2, GPT-5.2 Pro
    Open the source record
  • AI collaborating with humans

    Erdős AI contributions wiki · 27 Apr, 2026

    Machine
    GPT-5.5 Pro
    People
    Harjas Sandhu
    Open the source record
  • Formalization

    Erdős AI contributions wiki · 10 May, 2026

    Machine
    Codex, GPT-5.5 Pro
    Open the source record
  • argument

    VibeMathed

    Machine
    GPT-5.5 Pro
    People
    Harjas Sandhu
    Reported outcome
    resolved
    Open the source record

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