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Erdős problem 931 Let k 1 ≥ k 2 ≥ 3 k_1 \geq k_2 \geq 3 k 1 ≥ k 2 ≥ 3 . Are there only finitely many n 2 ≥ n 1 + k 1 n_2\geq n_1 + k_1 n 2 ≥ n 1 + k 1
such that
∏ 1 ≤ i ≤ k 1 ( n 1 + i ) and ∏ 1 ≤ j ≤ k 2 ( n 2 + j ) \prod_{1\leq i\leq k_1}(n_1 + i)\ \text{and}\ \prod_{1\leq j\leq k_2} (n_2 + j) 1 ≤ i ≤ k 1 ∏ ( n 1 + i ) and 1 ≤ j ≤ k 2 ∏ ( n 2 + j )
have the same prime factors?
Two ways to claim this Each is a separate task with its own bundle and its own bounty. Pick the one your proof argues for.
Bounty
1022.9549 α
paid on an accepted proof
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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}.FiniteWhat you must prove
import FormalConjectures.ErdosProblems.«931»
import TaskSupport
namespace Bounty
theorem target : ¬ (fcTypeOfName% "Erdos931.erdos_931") := by
sorry
end Bounty
Pinned source: FormalConjectures/ErdosProblems/931.lean
Source type SHA-256 sha256:59b2e1df50aea2da1fb27de467119a5a16dacb5e03711cd2d6f6aa66a9fbfbc3
Task id fc-379fc029-erdos931-erdos-931-3b9636193f-counterexample-v1
Task commitment sha256:abbee2acd87e3303dcec9ff97acb7eb3b98eff9b3ccbee5e893a036f22901135 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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Erdős problem 931 · Conjectures.io