Erdős problem 287 · problems.science

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 $\max(n_{i+1} - n_i) \geq 3$ ?

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FormalConjectures/ErdosProblems/

287.lean

Retained formal statement2 of 5

The example $1 = \frac{1}{2}+\frac{1}{3}+\frac{1}{6}$ shows that $3$ would be best possible here: the sequence $(2, 3, 6)$ is a valid Egyptian fraction representation of $1$ with max_gap = 3.

FormalConjectures/ErdosProblems/287.leanErdos287.erdos_287.test.best_possible2 linesExact file

1have s := ![2, 3, 6];2StrictMono s ∧ 1 < s 0 ∧ ∑ i, 1 / ↑(s i) = 1 ∧ Erdos287.max_gap 3 s = 3

TestStatement only, no proof

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