Number theory
$5,107 bountynobody has started
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
Even one lemma helps. Whoever finishes this later shares the pool with everyone who got them there.
contrib new erdos-931Command line, then a pull request on GitHub.
Nothing has been published against this problem yet.
A first lemma is worth as much as a last one: whoever closes the problem shares the pool with everyone who got them there.
Formal statement
Proof target
import FormalConjectures.ErdosProblems.«931»
import TaskSupport
namespace Bounty
theorem target : fcTypeOfName% "Erdos931.erdos_931" := by
sorry
end Bounty
Original conjecture (Lean type)
True ↔
∀ (k₁ k₂ : ℕ),
k₂ ≥ 3 →
k₂ ≤ k₁ →
{(n₁, n₂) |
n₁ + k₁ ≤ n₂ ∧
(∏ i ∈ Finset.Icc 1 k₁, (n₁ + i)).primeFactors = (∏ j ∈ Finset.Icc 1 k₂, (n₂ + j)).primeFactors}.FiniteOriginal conjecture source: FormalConjectures/ErdosProblems/931.lean
References
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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