Erdős problem 930 · problems.science

Is it true that, for every $r$ , there is a $k$ such that if $I_1,\ldots,I_r$ are disjoint intervals of consecutive integers, all of length at least $k$ , then $\prod_{1\leq i\leq r}\prod_{m\in I_i}m$ is not a perfect power?

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FormalConjectures/ErdosProblems/930.lean

Formal Conjectures

FormalConjectures/ErdosProblems/930.leanErdos930.erdos_9306 linesExact file

1True ↔2  ∀ r > 0,3    ∃ k,4      ∀ (I₁ I₂ : Fin r → ℕ),5        (∀ (i : Fin r), 0 < I₁ i ∧ I₁ i + k ≤ I₂ i + 1) →6          (∀ (i j : Fin r), i < j → I₂ i < I₁ j) → ¬Erdos930.IsPower (∏ i, ∏ m ∈ Finset.Icc (I₁ i) (I₂ i), m)

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