Erdős problem 287

Let $k\geq2$ . Is it true that, for any distinct integers $1 < n_1 < \cdots < n_k$ such that $\sum_{i=1}^k \frac{1}{n_i} = 1$ , we must have $\max(n_{i+1} - n_i) \geq 3$ ?

Sources

The source's own material, retained exactly.

5 retained statements36c6d0fef71a

FormalConjectures/ErdosProblems/

287.lean

Retained formal statement3 of 5

The lower bound of $\geq 2$ is equivalent to saying that $1$ is not the sum of reciprocals of consecutive integers, proved by Erdős [Er32].

FormalConjectures/ErdosProblems/287.leanErdos287.erdos_287.variants.gap_at_least_two1 lineExact file

1∀ (k : ℕ) (x : 2 ≤ k) (s : Fin k → ℕ), StrictMono s → 1 < s ⟨0, ⋯⟩ → ∑ i, 1 / ↑(s i) = 1 → 2 ≤ Erdos287.max_gap k s

SolvedStatement only, no proof