How Egyptians use this table to do division? Let's consider the following example:

Example 1.7.

Suppose we divide 131 by 25.

The sum is a bit long, isn't it? In fact, we can write 6/25 in a much simpler way: 1/25 + 1/ . Therefore, the method used by Egyptians possibly won't yield the shortest representation.

In fact, this is a conjecture according to Erdos and Straus about Egyptian fractions, which is still unsolved today:

For any positive integer n ≥ 2,

It is already known that the conjecture is true for n ≤ 10¹⁴!