A new algorithm for the expansion of Egyptian fractions

AbstractA rational number pq is said to be written in Egyptian form if it is presented as a sum of reciprocals of distinct positive integers, n1, n2,…, nk. The new algorithm here presented is based on the continued fraction expansion of the original fraction. It has the advantage of relatively short length, while keeping the ni below the very reasonable bound of q2. This method also ties in the best lower approximations to pq with the sub-sums of the Egyptian expansion. Because it is based on the continued fraction the method is extendable to irrational numbers