This presentation will delve into a fascinating open Erdös Problem, which poses the question: Is it true that there are no solutions to \(n! = x^k \pm y^k\) with $x, y, n, k \in \mathbb{N}$, $xy > 1$, and $k > 2$? We will show that a solution does indeed exist. However, in exploring whether this solution is unique, we uncover an intriguing pattern among the co-primes. This presentation will feature beautiful plots and reveal unexpected phenomena that invite deeper investigation. Join us as we navigate through these mathematical curiosities and uncover the hidden structures within.

The problem that we will discuss is given here: https://www.erdosproblems.com/go_to/399