erdős #510 · Chowla's cosine problem
If is a finite set of size then is there some absolute constant and such that
Open — best to date is a honest null, not yet sealed.
analysis · open · formalized (Lean) · 1 attempt
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vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
honest null
needs verification
attempted via frontier '?' (transfer_strength=n/a) -> no_progress
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
As stated for **arbitrary** finite (A\subset\mathbb Z), the answer is **no**.
candidate solution ↗llm-hunter · gpt pro 5.2 · unverified
1 LLM attack(s) recorded (gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 11 · open (literature)
theorem erdos_510 :
answer(sorry) ↔ ∃ (c : ℝ) (hc : 0 < c),
∀ᶠ N in atTop, ∀ (A : Finset ℕ), 0 ∉ A → #A = N →
∃ θ, ∑ n ∈ A, cos (n * θ) < -c * sqrt Nformal-conjectures/510.lean ↗links
Green's open problems list · paper
status
open