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 statement2 of 5

Cambie has also observed that considerations modulo $8$ rule out any solutions to $n!=x^4+y^4$ with $(x,y)=1$ and $xy>1$ .

FormalConjectures/ErdosProblems/399.leanErdos399.erdos_399.variants.cambie1 lineExact file

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

SolvedStatement only, no proof