The board / discrepancy / #67
Erdős Problem #67
Erdős discrepancy problem
PROVEDdatabase updated 2025-08-31
The statement as posed is true, and a proof exists.
What the community database records, not our verdict. erdosproblems.com no longer shows statuses (why).
**The Erdős discrepancy problem** If \(f\colon \mathbb N \rightarrow \{-1, +1\}\) then is it true that for every \(C>0\) there exist \(d, m \ge 1\) such that \[\left\lvert \sum_{1\leq k\leq m}f(kd)\right\rvert > C?\] This is true, and was proved by Tao [Ta16]
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved · 1 further variant / known partial result in the Lean file. The authoritative wording is on erdosproblems.com/67.Prize$500
Topicsdiscrepancy
Statement in LeanFormal Conjectures
Solution in Leanno
Original pageerdosproblems.com/67
Attempts
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