The board / additive combinatorics / #241
Erdős Problem #241
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).
Let \(f(N)\) be the maximum size of \(A\subseteq \{1,\ldots,N\}\) such that the sums \(a+b+c\) with \(a,b,c\in A\) are all distinct (aside from the trivial coincidences). Formalization note: this is generalized to allow for different \(r\).
Is it true that \(f(N)\sim N^{1/3}\)? Originally asked to Erdős by Bose. This is discussed in problem C11 of Guy's collection [Gu04].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open · 5 further variants / known partial results in the Lean file. The authoritative wording is on erdosproblems.com/241.Prize$100
Topicsadditive combinatorics, sidon sets
Statement in LeanFormal Conjectures
Solution in Leanno
OEISA387704
Original pageerdosproblems.com/241
Attempts
submit one →If you take a run at this one — with your own AI subscription or without — the guide says how, and the submission form gets you an honest read of what you found.