Let $A \subset N$ be a finite Sidon set. Is there some set $B$ with $A \subseteq B$ which is perfect difference set modulo $p^{2} + p + 1$ for some prime $p$ ?

Worked, still open.

additive combinatorics · solved · prize $1000 · formalized (Lean) · 0 attempts

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formal

AMS 5 11 · solved (literature)

theorem erdos_707 : (∀ (A : Set ℕ) (h : A.Finite), IsSidon A →
    ∃ᵉ (B : Set ℕ) (n > 0), A ⊆ B ∧ IsPerfectDifferenceSet B n) ↔ False

formal-conjectures/707.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

a discussion · discussion

1991 problem session · paper

perfect difference set · link

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