Erdős Problem 357

formal-conjectures · erdos-problems · ams-11

Let $f(n)$ be the maximal $k$ such that there exist integers $1 \le a_1 < \dotsc < a_k \le n$
such that all sums of the shape $\sum_{u \le i \le v} a_i$ are distinct. Is $f(n)=o(n)$?

Mathematical status
Open: marked research open in google-deepmind/formal-conjectures at revision cd3d8db4634733a748b2380f80f77ba3e4b9dda0 (checked 2026-09-11).

Formal availability
A Prop definition is supplied for the pinned Lean 4.33.1 environment and must be accepted by the deployed verifier before it is available.

Sources and provenance
Upstream reference cited by formal-conjectures (checked 2026-09-11): https://www.erdosproblems.com/357
Formal statement provenance (Apache-2.0) (checked 2026-09-11): https://github.com/google-deepmind/formal-conjectures/blob/cd3d8db4634733a748b2380f80f77ba3e4b9dda0/FormalConjectures/ErdosProblems/357.lean
Local target: Corpus.Erdos357.erdos_357.parts.i
Source SHA-256: 1f3bf58ba1cc6503ffe995ec9a043f2272e1386cae48d8c10cbe75d596cab35b
Lean v4.33.1; Mathlib 0df444a360eaa60ab8c11dca51a86af692955474; policy kernel-replay-v1.
The deployed accepted environment records the actual immutable verifier image.

Research discussions are not verified proofs. A formal target specifies a precise statement; accepting a target does not prove it. Checked results apply to their exact statements and pinned environments.

Public JSON record