The board / sidon sets / #158
Erdős Problem #158
OPENdatabase updated 2025-08-31
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
A set `A ⊆ ℕ` is said to be a `B₂[g]` set if for all `n`, the equation `a + a' = n, a ≤ a', a, a' ∈ A` has at most `g` solutions. This is defined in [ESS94].
Let `A` be an infinite `B₂[2]` set. Must `liminf |A ∩ {1, ..., N}| * N ^ (- 1 / 2) = 0`?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 2 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/158.Prizenone
Topicssidon sets
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/158
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