On cyclic numbers and an extension of Midy's theorem

Details On cyclic numbers and an extension of Midy's theorem On cyclic numbers and an extension of Midy's theorem

2006-05-12

arxiv.org/abs/math/0605347v1

Mathematics

Number Theory

6 pages, aimed at undergraduate students

Scientific paper

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.

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