Erdős problem 242 · problems.science

For every $n>2$ there exist distinct integers $1 ≤ x < y < z$ such that $\frac 4 n = \frac 1 x + \frac 1 y + \frac 1 z$ .

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FormalConjectures/ErdosProblems/

242.lean

Retained formal statement2 of 2

Schinzel conjectured (see [Si56]) the generalisation that, for any fixed $a$ , if $n$ is sufficiently large in terms of $a$ then there exist distinct integers $1\leq x < y < z$ such that $\frac{a}{n} = \frac{1}{x}+\frac{1}{y}+\frac{1}{z}.$

FormalConjectures/ErdosProblems/242.leanErdos242.erdos_242.variants.schinzel_generalization1 lineExact file

1∀ (a : ℕ), 0 < a → ∀ᶠ (n : ℕ) in Filter.atTop, ∃ x y z, 1 ≤ x ∧ x < y ∧ y < z ∧ ↑a / ↑n = 1 / ↑x + 1 / ↑y + 1 / ↑z

OpenStatement only, no proof

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