Is it true that there are no solutions to $n! = x^{k} \pm y^{k}$ with $x, y, n \in N$ , with $x y > 1$ and $k > 2$ ?

Worked, still open.

number theory · solved · formalized (Lean) · 0 attempts

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formal

AMS 11 · solved (literature)

theorem erdos_399 : answer(False) ↔
    ¬ ∃ (n x y k : ℕ), 1 < x * y ∧ 2 < k ∧ (n ! = x ^ k + y ^ k ∨ n ! + y ^ k = x ^ k)

solved