Egyptian fractions are an area of great interest to me. They show a bit of Ancient Egypt's history
and this history fascinates my imagination. I used the conjectures of two 20th century
mathematicians, Erdös and Sierpinski, on Egyptian fractions as a basis for my science fair project.
Their conjecture was the following: Is it possible to use Egyptian fractions to write all rational
numbers of the form 4/n or 5/n, where n is greater than or equal to 3, as a sum of three fractions,
1/a + 1/b + 1/c where a is less than b is less than c.