## 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.

**Comments:** 5 Pages.

**Download:** **PDF**

### Submission history

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

**Unique-IP document downloads:** 190 times

Vixra.org is a pre-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary.
In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution.
Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

**Add your own feedback and questions here:**

*You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.*

*
*