On cyclic numbers and an extension of Midy's theorem

Juan B. Gil; Michael D. Weiner

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On cyclic numbers and an extension of Midy's theorem

Juan B. Gil·Michael D. Weiner

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Abstract

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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Juan B. Gil, Michael D. Weiner. 2006-05-12. On cyclic numbers and an extension of Midy's theorem. https://arxiv.org/abs/math/0605347

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