Erdős problem 931 · problems.science

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?

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Browse retained paths and inspect the exact material available for this Problem.

4 retained statements2415f78e850a

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FormalConjectures/ErdosProblems/

931.lean

Retained formal statement3 of 4

In fact there exist counterexamples, like this one found by AlphaProof.

FormalConjectures/ErdosProblems/931.leanErdos931.erdos_931.variants.additional_condition_nonempty6 linesExact file

1∃ k₁ k₂,2  ∃ (_ : k₂ ≤ k₁) (_ : 3 ≤ k₂),3    {(n₁, n₂) |4        n₁ + k₁ ≤ n₂ ∧5          n₂ ≤ 2 * (n₁ + k₁) ∧6            (∏ i ∈ Finset.Icc 1 k₁, (n₁ + i)).primeFactors = (∏ j ∈ Finset.Icc 1 k₂, (n₂ + j)).primeFactors}.Nonempty

SolvedStatement only, no proof

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