Egyptian fractions raise many open problems; this is one of the most famous of them.

Suppose we wish to write fractions as sums of distinct unit fractions with odd denominators. Obviously, every such sum will have a reduced representation with an odd denominator.

For instance, the greedy algorithm applied to $\frac{2}{7}$ gives $\frac{1}{4}+\frac{1}{28}$, but we may also write $\frac{2}{7}$ as $\frac{1}{7}+\frac{1}{9}+\frac{1}{35}+\frac{1}{315}$.

It is known that we can we represent every rational number with odd denominator as a sum of distinct unit fractions with odd denominators.

However it is not known whether the greedy algorithm works when limited to odd denominators.