The Exact Computation of the Decompositions of the Recto Table of the Rhind Mathematical Papyrus

Abstract

The Rhind Mathematical Papyrus contains in the fragment known as the Recto Table the division of 2 by all the odd integer numbers from 3 to 101. This table hides the secret of how it was computed by its ancient Egyptian author because, till now, there is not a set of established known assumptions which allow compute all its values without any exception. In this paper, the algorithm which computes all the Recto Table is going to be established except three cases (denominators n = 35, 91 ad 95) which are calculated using another formula and the final denominator n = 101 which is a rareness.