If you want to explore Egyptian Fractions more, here is a paper focusing on the Erdős-Graham problem [1.]: "On a Coloring Conjecture about Unit Fractions" by Er

If you want to explore Egyptian Fractions more, here is a paper focusing on the Erdős-Graham problem [1.]: "On a Coloring Conjecture about Unit Fractions" by Ernest Croot [2.] [1.] https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Graham_problem https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93Graham_prob... [2.] http://arxiv.org/abs/math/0311421 http://arxiv.org/abs/math/0311421