From the Rhind Papyrus and other se

From the Rhind Papyrus and other sextant sources, we know that the ancient Egyptians were
very interested in expressing a given fraction into a sum of distinct unit fractions, that is,
fractions whose numerators are equal to 1. They even developed tables where in they tabulated
the unit fraction decompositions of specific fractions. One of the problems that has come down
to us in the last 60 years or so; is the problem of whether for each n ≥ 2; the fraction
4/n can be
decomposed as a sum of three distinct unit fractions. In otherwords, whether for each n ≥ 2; the
diophantine equation
4/n = 1/x + 1/y + 1/z has a solution in positive integers x, y and z ; with
x ≠ y , y ≠ z and z ≠ x . This problem is formally known as the Erdos-Strauss Conjecture, first
formulated in 1948, even though the earliest published reference to it appears to be a 1950 Paul
Erdos paper. Since 1950, a number of partial results have been obtained, for example see
references [1] – [10], [12] and [13]. In this work, we contribute four theorems, three of which
(Theorems 2,3, and 4) directly deal with the above problem.