The board / arithmetic progressions / #199
Erdős Problem #199
DISPROVED LEANdatabase updated 2026-02-24
The statement as posed is false. A solution has also been checked by machine, in Lean.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
If \(A\subset \mathbb{R}\) does not contain a 3-term arithmetic progression then must \(\mathbb{R}\backslash A\) contain an infinite arithmetic progression? Baumgartner [Ba75] answered this in the negative.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/199.Prizenone
Topicsarithmetic progressions
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/199
Attempts
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