On the decomposition of $1$ as the sum of Egyptian fractions with odd denominators Suppose that we decompose $1$ as a sum of Egyptian fractions with odd denominators.
I noticed (from a cursory view) that the fraction
$$\frac{1}{3}$$
appears in each of such decompositions.
Questions

Must the fraction $1/3$ appear in each such decomposition? Is it possible to prove this? Or is there a counterexample?


$1 = \frac{1}{5} + \frac{1}{7} + \frac{1}{9} + \frac{1}{11} + \frac{1}{13} + \frac{1}{15} + \frac{1}{17} + \frac{1}{19} + \frac{1}{21} + \frac{1}{23} + \frac{1}{25} + \frac{1}{27} + \frac{1}{33} + \frac{1}{611} + \frac{1}{265525} + \frac{1}{97544139723} + \frac{1}{8457652617058141652925}
$
