erdos_930.variant.consecutive_integers

Erdos and Selfridge [ErSe75] proved that the product of consecutive integers is never a power (establishing the case $r=1$). Theorem 1 from [ErSe75]. It is implied from `erdos_930.variant.consecutive_strong`. [ErSe75] Erdős, P. and Selfridge, J. L., The product of consecutive integers is never a power. Illinois J. Math. (1975), 292-301.

theorem erdos_930.variant.consecutive_integers :
    ∀ n k, 0 ≤ n → 2 ≤ k →
      ¬ IsPower (∏ m ∈ Icc (n + 1) (n + k), m)

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