# The Unit Fraction

For reasons which are not entirely clear to me the ancient Egyptians considered fractions $\frac{1}{b}$ much simpler than fractions of the form $\frac{a}{b}$ and they were interested in representing $$\frac{a}{b} = \frac{1}{x_1} + \cdots + \frac{1}{x_n}$$ where $a$ and $b$ are positive integers and $x_1 < x_2 \ldots x_n$ is an increasing sequence of integers.