The board / sidon sets / #152
Erdős Problem #152
PROVED LEANdatabase updated 2026-08-23
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
Define `f n` to be the minimum of `|{s | s - 1 ∉ A + A, s ∈ A + A, s + 1 ∉ A + A}|` as `A` ranges over all Sidon sets of size `n`.
Must `lim f n = ∞`? This was proved formally by the DeepMind prover agent [DM26a].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/152.Prizenone
Topicssidon sets
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/152
Attempts
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