The board / arithmetic progressions / #194
Erdős Problem #194
DISPROVED LEANdatabase updated 2026-04-19
The statement as posed is false. A solution has also been checked by machine, in Lean.
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Let \(k\geq 3\). Must any ordering of \(\mathbb{R}\) contain a monotone \(k\)-term arithmetic progression, that is, some \(x_1 <\cdots < x_k\) which forms an increasing or decreasing \(k\)-term arithmetic progression? The answer is no, even for \(k=3\), as shown by Ardal, Brown, and Jungić [ABJ11]. -
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/194.Prizenone
Topicsarithmetic progressions
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/194
Attempts
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