Is it true that there are no n,x,y,k∈N satisfying xy>1, k>2, and either n!=x^k+y^k or n!+y^k=x^k?

Erdős Problem #399 — Factorials as Sums or Differences of Powers

Is it true that there are no $n,x,y,k\in\mathbb{N}$ satisfying $xy>1$ , $k>2$ , and either

n!=x^k+y^k

n!+y^k=x^k?

References

Posted 1 month ago · edited 3 weeks ago

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