erdos_931

Specification

Let $k_1 \geq k_2 \geq 3$. Are there only finitely many $n_2\geq n_1 + k_1$ such that $$ \prod_{1\leq i\leq k_1}(n_1 + i)\ \text{and}\ \prod_{1\leq j\leq k_2} (n_2 + j) $$ have the same prime factors?

Actions

Submit a Proof

Have a proof attempt? Submit it for zero-trust verification.

Submit Proof

Lean 4 Statement

theorem erdos_931 : answer(sorry) ↔ ∀ᵉ (k₁ : 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 }.Finite

ID: ErdosProblems__931__erdos_931

Browse

All Problems

Explore all 300 unsolved conjectures.

View problems →

Docs

Verification Pipeline

How zero-trust verification works.

Read docs →

Evaluation Results

Recent Submissions

No submissions yet. Be the first to attempt this problem.