erdos_137.variants.perfect_power

Let $k\geq 2$. Erdős and Selfridge [ES75] proved that the product of any $k$ consecutive integers $N$ cannot be a perfect power. [ES75] P. Erdös, J. L. Selfridge, "The product of consecutive integers is never a power", Illinois J. Math. 19(2): 292-301, 1975

theorem erdos_137.variants.perfect_power (k : ℕ) (hk : k ≥ 2) (n : ℕ) (x l : ℕ) (hl : 2 ≤ l) :
    (∏ x ∈ Finset.Ioc n (n + k), x) ≠ x ^ l

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