Let $n \geq 4$ . Are there $n$ points in $R^{2}$ , no three on a line and no four on a circle, such that all pairwise distances are integers?

Open — best to date is a honest null, not yet sealed.

geometry · open · formalized (Lean) · 1 attempt

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

honest null

needs verification

attempted via frontier '?' (transfer_strength=n/a) -> already_known

No solve/partial on this pass. Transfer into the owned frontier was 'n/a'. Do not re-attack cold; needs a new idea or richer accumulated context.

unverified AI candidates (2)

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

This is a well-known Erdős problem about **planar integer-distance sets in general position** (no three collinear, no four cocircular).

llm-hunter · gpt pro 5.2 · unverified

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

AMS 52 · open (literature)

theorem erdos_213 : answer(sorry) ↔ ∀ n : ℕ, n ≥ 4 → Erdos213For n

open