Number Theory

   

Extended Midy's Theorem

Authors: Bassam Abdul-Baki

In mathematics, Midy's theorem, named after French mathematician E. Midy, is a statement about the decimal expansion of fractions a/p where p is a prime and a/p has a repeating decimal expansion with an even period. If the period of the decimal representation of a/p is 2n, then the digits in the second half of the repeating decimal period are the 9s complement of the corresponding digits in its first half. The Extended Midy's Theorem states that if the repeating portion of the decimal expansion of a/p is divided into k-digit numbers, then their sum is a multiple of 10^k − 1.

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[v1] 2013-05-13 06:47:57

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