The board / number theory / #34
Erdős Problem #34
DISPROVED LEANdatabase updated 2026-02-05
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).
The set of consecutive sums of a permutation `p` of `{1,…,n}`, where position `k` holds the value `p k + 1`: the sums `∑_{u ≤ k ≤ v} (p k + 1)`.
For any permutation \(\pi\in S_n\) of \(\{1,\ldots,n\}\) let \(S(\pi)\) count the number of distinct consecutive sums, that is, sums of the shape \(\sum_{u\leq i\leq v}\pi(i)\). Is it true that \[ S(\pi) = o(n^2) \] for all \(\pi\in S_n\)? Hegyvári [He86] gave a counterexample.
Statement as formalized in Formal Conjectures (Google DeepMind, Apache-2.0) · their label: research solved. The authoritative wording is on erdosproblems.com/34.Prizenone
Topicsnumber theory
Statement in LeanFormal Conjectures
Solution in Leanyes
Original pageerdosproblems.com/34
Attempts
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