ON MIDY'S THEOREM IN BASE b
Abstract.
In 1836 E. Midy proved that if the period of a reciprocal of a prime p ≥ 5 has even length and is split into two half-periods, then the sum of the halves is a string of 9's. This result has been generalized to any base b. In this note we give a very simple proof of this generalization.
AMS Subject Classification: 97F40, 11A05
Key Words and Phrases: Midy's theorem, repeating decimals
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DOI: 10.12732/ijam.v26i2.5
Volume: 26
Issue: 2
Year: 2013
