Erdős #357 (?, AMS 11). STATEMENT: 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. FORMAL: erdos_357: (fun n ↦ (f n : ℝ)) =o[atTop] (fun n ↦ (n : ℝ)); erdos_357: (answer(sorry) : ℕ → ℝ) =O[atTop] (fun n ↦ (f n : ℝ)); erdos_357: (fun n ↦ (f n : ℝ)) =O[atTop] (answer(sorry) : ℕ → ℝ) KNOWN/REMARKS: # Erdős Problem 357 *Reference:* erdosproblems.com/357 | 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 $f(n)=o(n)$? | Formalisation note: the next 5 formalisations are an attempt at capturing the question "how does $f(n)$ grow?". In addition to trivial solutions (e.g. setting RELATED: [] OEIS: []

id

vpr_b98abcaf6eeb35a4

frontier

Erdős problems frontier

kind

finding.add

created

2026-06-04