Erdős Problem #1125
PROVED LEANdatabase updated 2026-04-11
The statement as posed is true, and a proof exists. A solution has also been checked by machine, in Lean.
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Let \(f:\mathbb{R}\to \mathbb{R}\) be such that \[2f(x) \leq f(x+h)+f(x+2h)\] for every \(x\in \mathbb{R}\) and \(h>0\). Must \(f\) be monotonic? A problem of Kemperman [Ke69], who proved it is true if \(f\) is measurable. Erdős [Er81b] wrote 'if it were my problem I would offer \$500 for it'. This was solved by Laczkovich [La84].
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/1125.Prizenone
Topicsanalysis
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/1125
Attempts
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