Mapping Integers and Hensel Codes Onto Farey Fractions

Resumé

The order-N Farey fractions, where N is the largest integer satisfying N<= ˆ(p-1)/2, can be mapped onto a proper subset of the integers {0,1,...,p-1} in a one-to-one and onto fashion. However, no completely satisfactory algorithm for affecting the inverse mapping (the mapping of the integers back onto the order-N Farey fractions) appears in the literature.

A new algorithm for the inverse mapping problem is described which is based on the Euclidian Algorithm. This algorithm solves the inverse mapping problem for both integers and the Hensel codes.