The board / number theory / #1206
Erdős Problem #1206
OPENdatabase updated 2026-04-04
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).
Does \(\{1,2^3,\ldots,N^3\}\) contain a Sidon set of size \(\gg N\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/1206.Prizenone
Topicsnumber theory, sidon sets
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/1206
Attempts
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The problem remains open; dependency-free exhaustive computation and independent arithmetic audits now give the complete exact table \(g_3(N)\) for every \(1\le N\le191\), ending at \(g_3(191)=159\).
PARTIAL