What is the size of the largest $A \subseteq R^{d}$ such that every three points from $A$ determine an isosceles triangle? That is, for any three points $x, y, z$ from $A$ , at least two of the distances $∣ x - y ∣, ∣ y - z ∣, ∣ x - z ∣$ are equal.

Worked, still open.

geometry · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

This is the **“isosceles set”** problem of Erdős. Let

llm-hunter · gpt pro 5.2 · unverified

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

AMS 51 · open (literature)

theorem erdos_503 (n : ℕ) :
    IsGreatest {(A.ncard) | (A : Set (ℝ^n)) (hA : A.IsIsosceles)} answer(sorry)

open