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Can be partitioned into two sets, each of which can be permuted to avoid monotone 3-term arithmetic progressions?

Worked, still open.

arithmetic progressions · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239
vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

### What “avoid a monotone 3‑term A.P.” means

candidate solution ↗

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

candidate solution ↗

formal

AMS 5 · open (literature)

theorem erdos_197 :
    answer(sorry) ↔ ∃ A B : Set ℕ, IsCompl A B ∧
      (∃ f : ℕ ≃ A, ¬HasMonotoneAP (Subtype.val ∘ f) 3) ∧
      (∃ g : ℕ ≃ B, ¬HasMonotoneAP (Subtype.val ∘ g) 3)
formal-conjectures/197.lean ↗

status

open

notary

vela reproduce examples/erdos-problems
  • packet.json · sha256 6f179306a1409a8427e0eed2a9caee128f2bfdf0cdcb8df8f4542a9364fddd6b

finding.noted · reviewer:will-blair · 1 day

renders the record as of vev_d199cb2e · 1,338 events · hub

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