erdős #39
Is there an infinite Sidon set such thatfor all ?
Open — best to date is a honest null, not yet sealed.
number theory · open · prize $500 · formalized (Lean) · 1 attempt
machinery: Sidon/B_h,additive-combinatorics,greedy/probabilistic-construction,B_h-set-growth,number-field-construction
use this record
vela registry pull vfr_37aec80d874a0239vela reproduce examples/erdos-problemsevidence
honest null
needs verification
attempted via frontier 'sidon/B2' (transfer_strength=partial) -> no_progress
No solve/partial on this pass. Transfer into the owned frontier was 'partial'. 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 **open** (it’s one of Erdős’s longstanding problems on infinite Sidon sequences).
candidate solution ↗llm-hunter · gpt 5.2, gpt pro 5.2 · unverified
3 LLM attack(s) recorded (gpt 5.2, gpt pro 5.2); unverified.
candidate solution ↗formal
AMS 11 · open (literature)
theorem erdos_39 : answer(sorry) ↔ ∃ (A : Set ℕ), A.Infinite ∧ IsSidon A ∧
∀ᵉ (ε > (0 : ℝ)),
(· ^ (1 / 2 - ε) : ℕ → ℝ) =O[atTop] fun N => (((Set.Icc 1 N) ∩ A).ncard : ℝ)formal-conjectures/39.lean ↗links
Vela Sidon frontier (A309370) · verified work
A B₂/Sidon problem — the same object family as Vela's verified Sidon records, where nine improved terms were accepted into OEIS A309370 (the campaign's first external adoption).
OEIS A309370 ↗ · verified-combinatorics (witnesses + verify.py) ↗ · the Erdős campaign
status
open