Egyptian fractions for 2/105

The ancient Egyptians had a terrible notation for fractions. They had notations for for each , for , but everything else was written as a sum of these, with repeats forbidden, so that for example had to be written as . (Wikipedia) In an older article about Egyptian fractions and the Rhind Mathematical Papyrus, I said: Getting the table of good-quality representations of is not trivial, and requires searching, number theory, and some trial and error. It's not at all clear that . I think I see now where this comes from. , so two of the summands must have denominators divisible by and by respectively. The first thing you should do is consider $$\u5 + \u7 = \frac{12}{35} = \frac{36}{105}.$$ But you don't want , you want , so you multiply by : $$\u{18}\left(\u5 + \u7\right) = \u{90}+\u{126} = \frac 2{105}$$ and there it is. Why pick and rather than, say, and ? I suspect the answer is probably: Ahmes (or someone earlier) tried it both ways and picked the result they liked best. Remember…