Erdős problem 307 · problems.science

Are there two finite set of primes $P$ and $Q$ such that

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4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

307.lean

Retained formal statement3 of 4

Instead of asking for sets of primes, ask only that all elements in the sets be relatively coprime.

Cambie has found several examples when this weakened version is true. For example, $1=\left(1+\frac{1}{5}\right)\left(\frac{1}{2}+\frac{1}{3}\right)$ and $1=\left(1+\frac{1}{41}\right)\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{7}\right).$

FormalConjectures/ErdosProblems/307.leanErdos307.erdos_307.variants.coprime5 linesExact file

1True ↔2  ∃ P Q,3    0 ∉ P ∩ Q ∧4      1 < P.card ∧5        1 < Q.card ∧ (↑P).Pairwise Nat.Coprime ∧ (↑Q).Pairwise Nat.Coprime ∧ 1 = (∑ p ∈ P, (↑p)⁻¹) * ∑ q ∈ Q, (↑q)⁻¹

TextbookStatement only, no proof

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