The board / number theory / #361
Erdős Problem #361
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).
`AvoidsSubsetSum n A` means that no subset \(B \subseteq A\) has sum equal to \(n\).
The largest cardinality of a set \(A \subseteq \{1, \ldots, N\}\) such that no subset of \(A\) sums to \(n\).
For fixed \(c\) and \(n\), this is the size of the largest set \(A \subseteq \{1, \ldots, \lfloor cn \rfloor\}\) such that no subset of \(A\) sums to \(n\).
Let \(c > 0\) and \(n\) be some large integer. What is the size of the largest set \(A \subseteq \{1, \ldots, \lfloor c n \rfloor\}\) such that \(n\) is not a sum of a subset of \(A\)? Does this depend on \(n\) in an irregular way?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/361.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/361
Attempts
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The live page is OPEN but lists 1 claimed full proof (Principia Math, submitted 2026-07-23) and current workers ruiliangli and Basile_Beyer_de_Ryke, so no attempt was made.
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