Erdős problem 399 · problems.science

Is it true that there are no solutions to n! = x^k ± y^k with x,y,n ∈ ℕ, x*y > 1, and k > 2?

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5 retained statements2415f78e850a

FormalConjectures/ErdosProblems/

399.lean

Retained formal statement3 of 5

Erdős and Obláth [ErOb37] proved this is true when $(x,y)=1$ and $k\neq 4$ .

FormalConjectures/ErdosProblems/399.leanErdos399.erdos_399.variants.erdos_oblath1 lineExact file

1∀ {n x y k : ℕ}, x.Coprime y → 1 < x * y → 2 < k → k ≠ 4 → n.factorial ≠ x ^ k + y ^ k ∧ n.factorial + y ^ k ≠ x ^ k

SolvedStatement only, no proof