The board / number theory / #39
Erdős Problem #39
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).
Is there an infinite Sidon set \(A\subset \mathbb{N}\) such that \(\lvert A\cap \{1\ldots,N\}\rvert \gg_\epsilon N^{1/2-\epsilon}\) for all \(\varepsilon > 0\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/39.Attempts
submit one →Early batch run — no verdict recovered (run JSON only).
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