Bounds of the Denominators of Egyptian Fractions

A fraction (a/b) can be expressed as the sum of k unit fractions. Such representations are known as Egyptian fractions. In general, each a/b can be expressed by several different Egyptian fraction expnsions, so it is useful to be able to identify the bounds on the denominators. While bounds have been established for the general case where there is no restriction on the number of summands (k). For the specific case of k = 3 unit fractions, some of the existing bounds are improved and an upper bound for the largest denominator is estimated.