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erdos_137

Specification

Let $k\geq 3$. Can the product of any $k$ consecutive integers $N$ ever be powerful? That is, must there always exist a prime $p\mid N$ such that $p^2\nmid N$?

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Lean 4 Statement 
theorem erdos_137 : answer(sorry) ↔ ∀ k ≥ 3, ∀ n, ¬ (∏ x ∈ Finset.Ioc n (n + k), x).Powerful
ID: ErdosProblems__137__erdos_137
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