If you want to explore Egyptian Fractions more, here is a paper focusing on the Erdős-Graham problem [1.]: &quot;On a Coloring Conjecture about Unit Fractions&quot; by Ernest Croot [2.]<p>[1.] <a href="https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Erd%C5%91s%E2%80%93Graham_problem" rel="nofollow">https:&#x2F;&#x2F;en.wikipedia.org&#x2F;wiki&#x2F;Erd%C5%91s%E2%80%93Graham_prob...</a><p>[2.] <a href="http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;math&#x2F;0311421" rel="nofollow">http:&#x2F;&#x2F;arxiv.org&#x2F;abs&#x2F;math&#x2F;0311421</a>