The board / additive combinatorics / #155
Erdős Problem #155
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 size of the largest Sidon subset of \(\{1, \dots, N\}\).
Is it true that for every \(k \geq 1\) we have \[ F(N + k) \leq F(N) + 1 \] for all sufficiently large \(N\)?
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research open. The authoritative wording is on erdosproblems.com/155.Prizenone
Topicsadditive combinatorics, sidon sets
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/155
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.