The board / number theory / #329
Erdős Problem #329
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).
The partial density of a Sidon set `A` up to `N`, normalized by dividing by `√N` instead of `N`. This measures how close the set comes to the optimal density for Sidon sets.
The upper density of a Sidon set `A`, normalized by `√N`.
**Erdős Problem 329.** Let `A ⊆ ℕ` be a Sidon set. How large can `lim sup_{N → ∞} |A ∩ {1,…,N}| / N^{1/2}` be?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 4 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/329.Prizenone
Topicsnumber theory, sidon sets
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/329
Attempts
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Live page status is OPEN with 0 claimed proofs, but “Currently working on this problem” lists AnimishSharma (accessed 2026-07-28); per the no-collision rule, no attempt was made.
SKIPPED