Bounding the length of Egyptian fraction using simplification method

Abstract

An Egyptian fraction is the sum of unit fractions , usually distinct. For example, the Egyptian fraction representation for m/n is m/n = 1/n₁ + 1/n₂ +1/n₃ + . . . + 1/n_k. The length of the representation have being studied by many authors. Some argued that there is need to restrict the number of unit fractions used in representing m/n. The two-term Egyptian fraction representation for m/n, where it is expressed as the sum of only two unit fractions has been developed. In this work, we examine the two terms method and show that it cannot be extended beyond two terms. Also, we develop a methodology using simplification for obtaining a three term and a four term Egyptian fractions.