**Background:**

The Erdős–Straus conjecture, named after Paul Erdős and Ernest G. Straus, is a popular conjecture in number theory that states "For every integer n ≥ 2, there exist positive integers x, y, and z such that 4/n = 1/x + 1/y + 1/z."

For example, for n=5, 4/5 = 1/2 + 1/4 + 1/20 = 1/2 + 1/5 + 1/10. If x, y, and z were allowed to be positive and negative, the conjecture could be proved trivially, but restricting x, y, z to positive integers makes the problem a great challenge. Using computers, the conjecture has been verified up to n ≤ 10^14, but a proof for all n has not been provided yet.

**Your Task:**

Investigate the Erdős–Straus conjecture, and see if you can make any significant findings. While you're at it, you may want to research "Egyptian fractions", as these provide a helpful construct in understanding the conjecture. As always, comment your findings below!