On cyclic numbers and an extension of Midy's theorem
Juan B. Gil, Michael D. Weiner · arXiv (Cornell University) · 2006
In this note we consider fractions of the form 1/m and their floating-point representation in various arithmetic bases. For instance, what is 1/7 in base 2005? And, what about 1/4? We give a simple algorithm to answer these questions. In addition, we discuss an extension of Midy's theorem whose proof relies on elementary modular arithmetic.